Nash equilibrium is a game theory concept where optimal outcome is when there is no incentive for players to deviate from their initial strategy. 1 What Is Game Theory? Learning Objective 17. 2. •So Rose should switch to 1. You will also learn how to solve these games using Nashpy in python. , the network geometric structure), a necessary and sufficient condition is given to ensure the existence of local. 5 Advertising Game. Prince gets a tip about a potential mutiny. Fudenberg and Tirole - Game Theory. It was at the "Owls" retreat in the last episode. (1 – x)An optimal routing scheme in space information networks was presented to balance network loads for heterogeneous users. GTO stands for game theory optimal, and it’s a whole branch of mathematics. Game Theory Optimal. Game theory adopts a different perspective on optimization, as the focus is on the formation of beliefs about rivals’ optimal strategies. This interdependence causes each player to consider the other player’s possible decisions, or strategies, in formulating strategy. A relic of poker training from the 90’s is trying to understand what “level” players are playing at. optimal strategy given Player A’s strategy (the strategy with the minimum value in the row of the matrix). This is also called a normal-form representation of the game. A decision-making and game theory paradox that illustrates the decisions of two rational individuals cannot result in an optimal solution. Today, most university business students are introduced to the idea through the classic “prisoner’s dilemma. . Game Theory Optimal (GTO) is a term used to refer to a strategy that can’t be defeated. Lesson time 11:09 min. Nash equilibrium is the “Bedrock” of the Game Theory approach to Artificial Intelligence. A higher Price of Anarchy value implies a greater trade off between stability and optimality, and bounding the Price of Anarchy for a particular game puts a limit on this trade-off. This can be broken down mathematically pretty simply. The Nash equilibrium answers that by requiring that each firm's strategy be the best response to the other's strategies. A particular collection of interactivedecision situations arethe so-called. In this article, I’m going to explain what GTO is, why it’s popular, highlight why I think it isn. GTO means “Game Theory Optimal” and describes a “non-exploitable” strategy of poker play. First, we consider the representations of goals in terms of value functions that are prescribed by. In this memorable scene from “Star Wars,” our heroes, Luke. Show abstract. Game Theory. To those new. Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences. The rabbit’s strategy 65 3. The biggest problem with GTO strategies is that by definition. It is lower bounded by 1, a bound that it achieves only if all stable arrangements are optimal. And an algorithm that can find the game equilibrium point in polynomial time is. Optimal mechanisms are described as a research direction to optimize a performance metric such as the adversarial payoff functions in game theoretical adversarial deep learning. In my research, using big data and experiments, I try to answer two key. Recently the demand for more user-friendly methods to learn. Persaingan atau konflik ini dapat terjadi antara dua orang (dua pihak) atau sejumlah orang (grup). Although the theory of GTO has been discussed for many years, its popularity within poker is peaking right now. . e. He graduated summa cum laude with a Ph. S 0: The initial state of the game, which describes how it is set up at the start. We will discuss. A few years ago, solvers revolutionized how we learn, study and play poker, and we believe that Deepsolver is a game changer on the market. Its objective is to avoid strong assumptions about the opponent’s mistakes, and instead. •Then Rose should switch to 2. A key characteristic of. This is a similar outcome but for two firms that can keep prices high and stable or start a price war. 2 Analysis and results 2 1. It has applications in economics, logic, systems science and computer science. GTO (Game Theory Optimal) Strategy. Solve linear programming tasks offline! Game theory. going to a football game, going to a boxing match, or going for a hike. Selten developed the. (2020) at KIT on inverse optimal control and inverse reinforcement learning methods for parameter estimation in dynamic game theory. "Game Theory Optimal" — or "GTO" — is a term often heard in poker these days. Game Theory Optimal (GTO) poker is “an umbrella term players use to describe the holy grail of no-limit holdem playing strategy” (MasterClass). On the second day of the three. The game theory is used in a number of. If you play. Now let’s dive in. Game theory, as the mathematical branch, is completely useless for practical board game play, save for the most simple games. Synopsis: Chuck makes a daring and risky move to demonstrate his unwavering commitment to taking Prince down; Prince gets tipped off about a potential mutiny among his ranks; Wendy is tempted by a new opportunity. We set up a game theoretic framework to analyze a wide range of situations from team sports. If simultaneously have a row minimum and a column maximum this is an example of a saddle point solution. If player P1 pickssaid in an interview with Hart (2005): “game theory is optimal decision making in the presence of others with different objectives”. Game Theory is a branch of mathematics used to model the strategic interaction between different players in a context with predefined rules and outcomes. Improve this answer. However, the same choices for an individual robot may be less than optimal . This basically grants the user the power to freeze a certain strategy in a part of. The term Game Theory Optimal’, or ‘GTO’, is becoming more and more popular. Given the dynamics of poker, game theory is the ideal mathematical approach to identifying optimal decisions. If there exists more than one optimal strategy, running the program again may give another optimal strategy. My name is Sayan Chaudhuri and I am from India. Game Theory Optimal is a Small-sized Seller on Amazon's North America Marketplaces under the brands of USAOPOLY, ktopnob, LAVA, Fun Express, LatchKits, Bruder, Schylling And Star Magic. Chuck makes a daring and risky move to demonstrate his unwavering commitment to taking Prince down. Player P1 has m possible moves (pure strategies) and player P2 has npossible moves (pure strategies). In an environment in which many outcomes are pre-determined when sophisticated players follow their best strategies, the way to improve one's payoff is to change the actual structure of the strategic interactions before the game is even played. Game theory - Strategies, Equilibrium, Payoffs: The simplest game of any real theoretical interest is a two-person constant-sum game of perfect information. Constant sum: A game is a constant sum. The game theory is widely applied to study human as well as animal behaviours. A Game Theory Optimal solver is an algorithm that calculates the best possible poker strategy. An optimal strategy is one that provides the best payoff for a player in a game. It’s a defensive strategy that assumes your opponent is playing less than optimally. super optimal. Chuck makes a daring and risky move to demonstrate his unwavering commitment to taking Prince down. GTO is something every trader should understand. We now have “Game Theory Optimal” (GTO) solutions to poker, which include the ranges that are described by preflop poker charts. This article aims to capitalize on game theoretic techniques for optimal service marketing decision based on existing literature review. Think game theory is abstract and incomprehensible? Think again! Play Optimal Poker shatters the myth that game theory is only for elite poker players. Existing research contributions demonstrate that game theory is a potential approach to improve results in deep learning models. The model is considered an. In other words, if you play a perfect GTO. A poker hand is usually a configuration of five cards depending on the variant, either held entirely by a player or drawn partly. Chuck makes a daring and risky move to demonstrate his unwavering commitment to taking Prince down. Theory of Games and Economic Behavior: 60th Anniversary Commemorative Edition. Nash Equilibrium is an action chosen by each player such that: “No player would want to change their action. A Brief Introduction to Game Theory. This is a massive problem for GTO poker. Today we’ll be debunking 4 big myths about game theory optimal poker strategy, or “GTO,” as it’s now commonly called. In the case where the optimal policy is stochastic, the value of a state is harder to calculate. Instead, every player accurately expects the strategic choice of all other players. The theory of games started in the 20th century and it was proposed by John Von Neuman. You need only enter the non-zero payoffs. But now. Most games that. as depicted in Figure 4b, stands in stark contrast to the optimal management (Figure 4a, where µ is the shadow value of the stock, i. 8 p − 4 ( 1 − p) = − 2 p + 20 ( 1 − p) ⇒ p = 12 17. But how exactly do these solvers work? What makes their. i. It is widely used in two player turn-based games such as Tic-Tac-Toe, Backgammon, Mancala, Chess, etc. The software will set the others to zero. In [31], security game is proposed under the condition that strong assumption for unknown attacker is relaxed. Your assertion that game theoretic strategies are not useful because people are non-optimal is flatly wrong. Note the time it takes for an accumulation of 50% of the contestants to quit vs. A dominant strategy occurs when there is an optimal choice of strategy for each player no matter what the other does. It got user’s gain to decide. Game Theory can be applied in different ambit of Artificial Intelligence: Multi-agent AI systems. Aired: October 6, 2023. Our Random Number Generator, generates a random number every 30 seconds, so you can make the most Game Theory Optimal Poker decision in every pre-flop situation. 2. We will solve and analyze games through game theory by using di erent decision methods, decision trees, and the process of domination and simpli cation. Design your own exercises and systematically work on becoming a GTO expert. A poker hand is usually a configuration of five cards depending on the variant, either held entirely by a player or drawn partly from a number of shared,. ' In poker, this term gets thrown around to signal a few different. Renowned poker pro and coach Andrew Brokos takes you step-by-step through the fundamentals, explaining core game theory principles and how to apply them in real. Level-based thinking starts with you considering only your own hand. Assuming a system level object is given, the utility functions for individual agents are designed to convert a multiagent system into a potential game. Pareto Optimal. ) Tested on Mozilla, Netscape, Internet Explorer. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Equilibrium is a concept of game theory where each player in the game arrives at their optimal outcome. Considering the advantage, the mathematical model based on game theory strategy has been utilized for balancing tasks load among physical hosts in Cloud Data Center such that every host and users are benefitted. The user can collect the value Vi + min (F (i+2, j), F (i+1, j-1) ) where [i+2,j] is the range of. Today we’ll be debunking 4 big myths about game theory optimal poker strategy, or “GTO,” as it’s now commonly called. First, > it provides a way to precisely define and analyze strategic interactions, which can be complex and difficult to describe in natural language. ,xn) x = ( x 1, x 2,. . Chuck makes a daring and risky move to demonstrate his unwavering commitment to taking Prince down. Chuck: The practice of making sure that a guilty man goes down whether the evidence exists or needs to be. In the multi-party non-cooperative game called trading, stock exchange trading rules play a major role in determining ecosystem equilibrium. 2 Single Play Games. It is used to protect yourself rather than attack other players. Billions Season 7 Episode 9 -- Game Theory Optimal. a gonzo selection. Game Theory provides models for conceptualizing interactions among competing individuals: rules to follow, opponents to compete and teammates to cooperate with. The WPT GTO Trainer allows you to rapidly plug leaks and learn the Game Theory Optimal strategies that have dominated the highest stakes games in the world. A researcher has solved a nearly 60-year-old game theory dilemma called the wall pursuit game, with implications for better reasoning about autonomous systems such as driver-less vehicles. (d) The optimal strategy for Cis a pure strategy of 0 1 . This subject seems to confuse a lot of you guys based on how often I hear it asked about and mis-used. Modern game theory was introduced in the works of John von. We will also discuss why and when players use GTO in poker and how you can use the modern theory of poker to direct your decisions. Think of this week’s episode of “Billions” as the Death Star trash compactor. Using game theory, real-world. This poker software training tool combines the best simulator software with the best GTO calculator so that you can analyzing specific scenarios and learn the correct plays. Put each row on a new line. It is based around an in. The foundation of auction theory from a game theoretic perspective has provided an elegant analytical approach for understanding competitive bidding. Brams) •Suppose Colin and Rose both are thinking of choosing 1. It has widespread applications and is useful in political scenarios, logical parlour games, business as well as to observe economic behaviour. Determining the optimal privacy policy is modeled as a constrained minimax game between a privatizer and an adversary. Rubinstein and Osborne - A Course in Game Theory. Every player or agent is a rational entity who is selfish and tries to maximize the reward to be obtained. The Nash equilibrium is a key concept in game theory, in which it defines the solution of N-player noncooperative games. wikipedia. Game theory decision making is a helpful way to create strategies. S7 E9 58M TV-MA D. The sum of the change in utility. Abstract. (Cheat, Cheat) b. It doesn't need a lot of computing power, has an intuitive interface and is. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programming. The concepts of GTO are a perfect match for poker. Season 7, Episode 9: ‘Game Theory Optimal’. The first publicly available solver, PioSolver, which is also the most used, came out back in 2015. Game Theory Optimal is the ninth episode of the Season 7 of Billions. Season 7 Episode 9: Game Theory Optimal Aired : October 6, 2023 Synopsis : Chuck makes a daring and risky move to demonstrate his unwavering commitment to taking Prince down; Prince gets tipped off about a potential mutiny among his ranks; Wendy is tempted by a new opportunity. Here is a little on-line Javascript utility for game theory (up to five strategies for the row and column player). A discussion of how these solvers work is beyond the scope of the present article, but an excellent. It is played between two players, Even and Odd…. The value of the game is the optimal payoff. Luis Gomes, Zita. Modern game theory began in 1928, with John von Neumann’s proof of the existence of mixed strategy equilibria in zero-sum two-person games [7]. Algorithmic game theory (AGT) is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments. K. a. or. The payofffrom each of these alternatives will depend on the weather. The size is being reduced to just simplify the problem. [11] proposed a two-stage game model to provide the optimal security detection strategy for heterogeneous network systems; Li et al. First, an uncertain linear quadratic differential game model under optimistic value criterion was introduced and its analytic optimal controls were displayed. Over 1. Simple GTO Trainer — Master Game Theory Optimal play with this training tool. Optimal sale is the maximum profit that the firm can obtain under its. It conceives the idea of a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. Thus a game is any situation in which two or more players, not having identical interest, can affect the outcome. I need to show that the game has no saddle point solution and find an optimal mixed strategy. 4 Exercises 7 2 Utility theory 9 2. 3 The axioms of utility theory 14 2. This link is an example of such strategy regarding Pre-Flop Raises, Re-Raises, Re-Re-Raises and the corresponding reactions to each of them. 3. A GTO strategy is an entirely unbeatable poker strategy that represents a mathematically perfect way of playing poker. It seeks to “solve” the game of poker and provide an unexploitable strategy that offers the optimal solution to any given situation. Game theory helps one to develop optimal strategies. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower. org. A discussion of how these solvers work is beyond the scope of the present article, but an excellent. Recap Pareto Optimality Best Response and Nash Equilibrium Mixed Strategies Defining Games I Finite, n-person game: hN,A,ui: I N is a finite set of n players, indexed by i I A = A 1,. Today, deep learning is a fast-evolving area for research in the domain of artificial intelligence. What to do: Enter or paste your matrix in the first text box below. Corral – Wags crossing over enemy lines by going to Chuck’s SDNY office felt gunsling-y without the pistols. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. Check Price on Amazon. Texas Hold’em is a complicated game, and the best approach is to use GTO as your starting point and adjust to exploitative play when you have information on your opponents. Some examples 74 4. In practise, a lot of it involves guessing what your opponent will do next (and stopping your opponent guessing what you would do next). StatsResource. Ryan Harrington, a leading professional and instructor in the industry, will lead you through each step of understanding core game theory. For the past 10 years, I have been researching optimal decision-making. Alternatively, game theory has been showing its multi-dimensional applications in the last few decades. In other words, game theory is concerned with specifying actions for all players, ensuring that for each player, his/her chosen actions are optimal, given the actions of other. Play Optimal Poker: Practical Game Theory for Every Poker Player, a 237-page primer in practical game theory, equips readers to make better decisions under conditions of uncertainty. 3 Remarks 7 1. your opponent, it’s not taking into consideration the possibility that your opponent is a calling station. Game theory is an effective tool to investigate real-world scenarios with multiple stakeholders interacting with each other. You can check out more at: (Game Theory Optimal) play explained in 15 minutes. Game Theory Optimal Poker Solvers Explained This paper provides a comprehensive overview of the applications of game theory in deep learning. Outcomes in million USD. Game Theory Optimal (GTO) poker is “an umbrella term players use to describe the holy grail of no-limit holdem playing strategy” (MasterClass). 3. For that reason, game theory has become an essential tool to analyze modern energy systems. 1. Evolutionary game theory focuses on populations that repeatedly play games rather than individuals. G. Game theory applies to many different disciplines and the ‘GTO’ term has become popular in the poker world during the last decade. . Play. D. General-sum games with more than two players. He argued that certain predator–prey interactions, such as those between mimetic butterflies and bird predators, could be understood using. be the probability of selection of alternative 1 by player A and. Share. “Game Theory” is an analysis of strategic interaction. Originally formulated for. Named after Vilfredo Pareto, Pareto optimality is a measure of efficiency. Game Theory Optimal doesn’t take into account the opposing player’s tendencies. Minimax is a kind of backtracking algorithm that is used in decision making and game theory to find the optimal move for a player, assuming that your opponent also plays optimally. A solution to a game describes the optimal. 5% of BTN's flop range. Their existance has drastically changed the way poker strategy is understood. 2 Game Theory & Stock Market The stock market decisions everyday investors or speculators make in terms of di erent investment strategies and di erent players (investors). Time Travel to 1881 O. 2. Thus, game theory cannot prescribe an optimal action for an individual player without also offering a way for each player to anticipate what other players would choose. To solve a game, one needs to reduce a complex. A game theory optimal (GTO) poker strategy is referred to as the holy grail of no-limit Holdem playing strategy. p_n)$ can be expressed as a polynomial (quadratic) function of $(p_1, p_2,. Instead of assuming a single stakeholder as in centralized models, we consider different stakeholders, including the upstream shale gas producer and the midstream shale gas processor. It is well known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. In the spirit of ELI5, Game theory is very simply the mathematical study of social interactions (or social dynamics). As poker strategy evolved, many of the game’s best players began focusing on what was game theory optimal and used “solvers” to help them improve their game from a theoretical standpoint. We review the results of a research programme exploring how. Math is important in game theory for several reasons. Get Bonus £400. I have spent a huge amount of time trying to find the mixed strategy equilibria of this game, and unfortunately, I keep getting to no answer. Game theory was introduced in the previous chapter to better understand oligopoly. A Game Theory Optimal solver is an algorithm that calculates the best possible poker strategy. In the setting of a 1 vs 1 video games: In theory, it would help with getting the optimal strategy. He was a founder of game theory, which models rational choice in these interactions as maximization of some payo function. Most situations that use Game Theory involve at least two opposing parties. Relation to Psychology. Given a hand, there is a certain probability of your opponent having a better hand. The Nash Equilibrium in Game Theory. [1] The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. For both the players, the total probability is 1. 1. A pursuit-evasion game: Hunter and Rabbit 62 3. 1 The formulation of two-person games There are two players in this type of games, each has. 99/month thereafter. A game theory optimal solution to a game has precise mathematical definitions. Our Unbiased Game Theory Optimal Review Is Game Theory Optimal Legit on Amazon? Yes. A key characteristic of game theory is that a player’s payoff is dependent on the strategy of other players. Understanding GTO means you will need to start understanding some fundamentals in poker. Recall the definition of game theory. •If she does, then Colin should switch to 2. GTO stands for Game Theory Optimal. Nash Equilibrium in Poker. With Ryan Harringtons' book "Poker Strategy: Mastering the Fundamentals of Game Theory Optimal" we can finally put to rest the belief that game theory is only suited for experienced poker players. 1. standard play? This paper will explore the key considerations of making game theory optimal (GTO) plays in heads-up (two player) no limit Texas hold’em. He regularly final tables big online tournaments. This link is an example of such strategy regarding Pre-Flop Raises, Re-Raises, Re-Re-Raises and the corresponding reactions to each of them. Nash Equilibrium in Poker. In the following two questions, suppose we replay Bob and Al’s scenario with slightly different payoffs. 12 Exercises 509 13 Repeated games 519 13. Ranges are just a certain selection of hands that a player can have at a particular moment in the game. 2. Written by: Beth Schacter. TTC is optimal in the sense that it is both DSIC and that it produces the unique core allocation. 17. While GTO has its foundations hardcore math, exploitative poker is more about guessing your opponent’s tendencies. I could even imagine the smell of Michter’s whiskey on Wags’ breath that he downed for. A starting point of this theory is the zero-sum game. That buzz is GTO. Introduction to Game Theory 15 Odd-Even game Theory of Moves (Steven J. The optimal strategy for a population of agents is the one that minimizes the expected loss or cost. 1 Answer. Game theory optimal (GTO) poker is a term advanced poker strategists coined some years ago to essentially create perfect poker playing. Ryan Harrington, a leading professional and instructor in the industry, will lead you through each step of understanding core game theory. Cutting Edge Our GTO Poker Charts ranges were created by working through as many preflop scenarios as possible in different Poker Formats, using both Monker Solver and Pio Solver. GTO Poker (game theory optimal poker) is a style of playing poker that is based entirely on mathematics and is designed to make your plays unexploitable. Game theory - Strategies, Equilibrium, Payoffs: The simplest game of any real theoretical interest is a two-person constant-sum game of perfect information. The resulting evolutionary game theory mathematics lead to an optimal strategy of timed bluffing. ; Player (s): Defines which player in a state has the move. the dominant strategy. Payoff matrix 4 7!" "!1 "2 !7 "4 !5 "1 !5 "4 L L R L R R 4 5 1 5 2 1 L R L R! "A match is man-optimal if it is stable and there is no other stable match that some man prefers. We analyze Bitcoin mining from the perspective of a game and propose an optimal mining model that maximizes profits of pools and miners. I came across the concept of Game Theory when I was listening to a podcast interviewing Naval Ravikant. GAME THEORY ClassnotesforMath167,Fall2000 ThomasS. Therefore the best value that Player can achieve is the maximum over all the rows of the minimum values across each of the rows: • The corresponding pure strategy is the optimal solution for this game It is the optimal strategy for AThe dominant strategy in game theory refers to a situation where one player has a superior tactic regardless of how the other players act. So, how is it measured? Through a carefully curated card matrix, players can make the best decision with the focus on. If P2 chooses left P1 will choose. The theory introduceFrom player 1's perspective, if player 2 calls a fraction p p of the time, then player 1 should always bluff if p < 0. Equation (7) connects with the Optimal transport theory, and has a gradient ow interpretation in geometry. So. In order to simplify the forms of optimal controls, we formulated an uncertain linear quadratic differential game model with constrained parametric control domain. Which of the following circumstances in an industry will result in a Nash equilibrium? a. Some examples of "games" include chess. Wendy is tempted by a new opportunity. Other articles where optimal strategy is discussed: game theory: Games of perfect information:. N-player game, one strategy choice S i for each player i, is called a (Pure Strategy) Nash equilibrium if no player i perceives any feasible way of achieving a higher payo by switching unilaterally to another strategy S0 i. A Stackelberg game has two players: one is the leader who takes its action first; the other one is the follower who takes its action after observing the leader’s response []. The optimal strategies to a matrix game turn out be solutions to linear programming problems. Stable Matching and Kidney Exchange. c. Students give MasterClass an average rating of 4. read press release. A solution to a game describes the optimal decisions of the players, who may have similar, opposed, or mixed interests, and the outcomes that may result from these decisions. A. Think game theory is abstract and incomprehensible? Think again! Play Optimal Poker shatters the myth that game theory is only for elite poker players. Selten developed the. 1 Pengantar Game Theory Dalam kehidupan sehari-hari sering dijumpai kegiatan-kegiatan yang bersifat kompetitif yang diwarnai persaingan atau konflik. Result (s, a): A transition model that defines a move’s outcome. Luckily, I know a thing or two about high-stakes decisions. Their existance has drastically changed the way poker strategy is understood. In the context of game theory, the idea of political parties trying to “game” the system is often too real; for example, gerrymandering is a corrupt behavior in the American system, but that doesn’t mean it isn’t the optimal strategy for winning elections. Therefore, players who implement GTO in their game will allow their opponents to make. How Game Theory Changed Poker Professional players are learning from computers how to make their play more unpredictable and harder to beat. Game theory is a branch of mathematics that studies interactions between the participants of the competition in specific settings. This chapter discusses how game theory can be used to speculate rival’s response to price change given some rational behavioral assumptions. If you’re following Game Theory Optimal and it says that you should put out a big bluff on the river vs. Game theory is thought to apply to any situation with two or more players where there are. The story of this episode was written by Beth Schacter and directed by Shaz Bennett. 4. It is applied in the study of sociological, political and psychological behaviours. Game Theory—the study of rational choice in interactive decision problems—has proved to be a significant tool for both normative and descriptive research on collective action problems. It isn’t optimal in theory, but in practice, the advantage to be gained is huge. 4. According to the competition among the nodes, the model was built based on queuing game theory. Wendy is tempted by a new opportunity. There is one optimal strategy for each player irrespective of what strategy the other player adopts. Andrew finished three times in the Top 100 in the World Series of Poker Main Event. There seems to be no stable solution!Matching pennies is the name for a simple game used in game theory. It allows decision making based on the inferences from the data in the most optimal way possible based on the inferences made after undertaking Big Data Analytics. The main intellectual attraction of the game theory is essentially a question of how to act in gaming situations against highly rational opponents A kind of static, finite and non-cooperative game. War of attrition for different values of resource. We develop categorical as well as continuous models, and obtain optimal.