Sample Chapter for Behavioral Game Theory: Experiments in Strategic Interaction by Camerer, C.F., published by Princeton University Press. Over the last 50 years, the theory of rational choice has emerged as the dominant. In response to empirical. Game theory question to test up to A Level and high school standard economics. We can solve the equilibrium by finding the best response of each player, conditional on each of the other player’s strategies: (a) When the pitcher chooses to throw a strike, the batter gets a payoff of 3 by taking, which. This article sketches the basic concepts of the theory of games in order to discuss some of their philosophical implications and problems. Consider the following situation: when two hunters set out to hunt a stag. The Games Economists Play - Implications of Economic Game Theory for the Study of Computer Games by Jonas Heide Smith. It is a source of confusion that economists for decades have worked on 'game theory' while. Clifford's 60 second explanation of how to identify the dominant strategy with game theory payoff matrix. The numbers in the left of each square are for the firm on the left. The numbers on the right are for the. Evolutionary game theory - Wikipedia. Evolutionary game theory (EGT) is the application of game theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. EGT originated in 1. John Maynard Smith and George R. Price's formalisation of the way in which such contests can be analysed as . It has been particularly helpful in establishing the basis of altruistic behaviours within the context of Darwinian process. Despite its origin and original purpose, evolutionary game theory has become of increasing interest to economists, sociologists, anthropologists, and philosophers. The problem. Haldane(as quoted by John Maynard Smith)The need for evolutionary game theory in biology started with a problem. The problem was how to explain ritualized animal behaviour in a conflict situation; . Tinbergen proposed that such behaviour exists for the benefit of the species. Maynard Smith couldn't see how this reasoning matched with Darwinian thought as he understood it. Maynard Smith, a former engineer and highly competent mathematician, turned to game theory to answer the question. A contest involves a number of players, all of whom have a choice of moves for the game. Games can be a single round or repetitive. Objective(s) Location Solution method Analysis type Game theory classification Citation; Fair allocation of water resource development costs to urban and agricultural sectors: Japan: Cooperative solution concept: Quantitative. The approach a player has in making his or her moves constitutes the player's . Rules govern the outcome for the set of moves taken by the players and outcomes produce payoffs for the various players; rules and resulting payoffs can be expressed as decision trees or in a payoff matrix. Classical game theory essentially requires that all of the players make rational choices (that is, making their strategic choice on a wholly rationally determined evaluation of probable outcomes). As a consequence, it is fundamental in game theory that each player must consider the strategic analysis that the players' opponents are making in determining that his or her own strategic choice is appropriate. Adapting game theory to evolutionary games. The results of the game will test how good that strategy is. That is what evolution does . In biology, strategies are genetically inherited traits that control an individual's action . The key point in the evolutionary game theory model is that the success of a strategy is not just determined by how good the strategy is in itself, it is a question of how good the strategy is in the presence of other alternative strategies, and of the frequency that other strategies are employed within a competing population. It is also a question of how good a strategy plays against itself, because in the biological world a successful strategy will eventually dominate a population and competing individuals in it end up facing identical strategies to their own. It is always a multi- player game with a very large population of competitors. Rules describe the contest as in classical Game Theory but for evolutionary games rules include the element of replicator dynamics, in other words the general rules say exactly how the fitter players will spawn more replicas of themselves into the population and how the less fit will be culled out of the player population (expressed in a Replicator Equation). Similarly, Evolutionary Game Theory only uses asexual reproduction for the sake of simplicity. Games are run repetitively with no terminating conditions. The results that are studied include the dynamics of changes in the population, the success/survival of strategies, and any equilibrium states reached. Unlike in classical Game Theory, players do not choose their strategy or have the ability to change it, they are born with that strategy and their offspring will inherit that same identical strategy. The Evolutionary game model Evolutionary game theory transposes Darwinian mechanisms into a mathematical form by adopting a System Model of evolutionary processes with three main components - Population, Game, and Replicator Dynamics. The system process itself has four phases: 1) The model (as evolution itself) deals with a Population (Pn). The population will exhibit Variation among Competing individuals. In the model this competition is represented by the Game. The Game tests the strategies of the individuals under the . These rules produce different payoffs . The contesting individuals meet in pairwise contests with others, normally in a highly mixed distribution of the population. The mix of strategies in the population affects the payoff results by altering the odds that any individual may meet up in contests with various strategies. The individuals leave the game pairwise contest with a resulting fitness determined by the contest outcome . This overall process then produces a New Generation P(n+1). Each surviving individual now has a new fitness level determined by the game result. The new generation then takes the place of the previous one and the cycle begins again (and never stops). Mathematically speaking it is an Iterative process. Over time the population mix in such a system may converge to a stationary state . Therefore, it is a major vehicle to help understand and explain some of the most fundamental questions in biology including the issue of group selection, sexual selection, altruism, parental care, co evolution, and ecological dynamics. Much of the progress in developing understanding in these diverse areas has been aided by evolutionary game theory modelling and many of the counter intuitive situations in these areas have been explained and put on a firm mathematical footing by the use of these models. The common methodology to study the evolutionary dynamics in games is through replicator equations. These replicator equations in the context of evolutionary biology show the growth rate of the proportion of organisms using a certain strategy and that rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole. The attractors (stable fixed points) of the equations are equivalent with evolutionarily stable states. A strategy which can survive all . In the context of animal behavior, this usually means such strategies are programmed and heavily influenced by genetics, thus making any player or organism's strategy determined by these biological factors. To achieve a better feel for the challenges of these different situations, evolutionary games are often given rather colourful names and . It all helps develop a feel for the mathematics of the game and the problems the players face. Some representative games of evolutionary game theory are hawk- dove, war of attrition, stag hunt, producer- scrounger, tragedy of the commons, and prisoner's dilemma. Some of the various strategies that apply in these games are Hawk, Dove, Bourgeois, Prober, Defector, Assessor, and Retaliator. Depending on the particular . The fitness of a Hawk for different population mixes is plotted as a black line, that of Dove in red. An ESS (a stationary point) will exist when Hawk and Dove fitness are equal: Hawks are 2. Doves are 8. 0% of the population. The most classic game (and Maynard Smith's starting point) is the Hawk Dove game. The game was conceived to analyse the animal contest problem highlighted by Lorenz and Tinbergen. It is a contest over a shareable resource. The contestants can be either a Hawk or a Dove. These are not two separate species of bird; they are two subtypes of one species with two different types of strategy (two different morphs). The term Hawk Dove was coined by Maynard Smith because he did his work during the Vietnam War when political views fell into one of these two camps. The strategy of the Hawk (a fighter strategy) is to first display aggression, then escalate into a fight until he either wins or is injured. The strategy of the Dove (fight avoider) is to first display aggression but if faced with major escalation by an opponent to run for safety. If not faced with this level of escalation the Dove will attempt to share the resource. Payoff Matrix for Hawk Dove Gamemeets Hawkmeets Doveif Hawk. V/2 - C/2. Vif Dove. V/2. Given that the resource is given the value V, the damage from losing a fight is given cost C: If a Hawk meets a Dove he gets the full resource V to himself. If a Hawk meets a Hawk . But that population makeup in turn is determined by the results of all of the previous contests before the present contest- it is a continuous iterative process where the resultant population of the previous contest becomes the input population to the next contest. If the cost of losing C is greater than the value of winning V (the normal situation in the natural world) the mathematics ends in an ESS . The population will progress back to this equilibrium point if any new Hawks or Doves make a temporary perturbation in the population. The solution of the Hawk Dove Game explains why most animal contests involve only . The result does not at all depend on . In the case where the resource is not sharable but an alternative resource might be available by backing off and trying elsewhere, pure Hawk or Dove strategies become less effective. If an unshareable resource is combined with a high cost of losing a contest (injury or possible death) both Hawk and Dove payoffs are then further diminished. A safer strategy of lower cost display, bluffing and waiting to win, then becomes viable . The game then becomes one of accumulating costs, either the costs of displaying or costs of prolonged unresolved engagement. Note the time it takes for an accumulation of 5. Therefore, only a random unpredictable strategy can maintain itself in a population of Bluffers. The contestants in effect choose an . This implements a distribution of bids for a resource of specific value V, where the particular bid made for any specific contest is chosen at random from within that distribution. The distribution (an ESS) can be computed by invoking the Bishop- Cannings theorem, which holds true for any case of mixed strategy ESS.
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