Stochastic game

About: Stochastic game is a research topic. Over the lifetime, 9493 publications have been published within this topic receiving 202664 citations.

Evolutionary game dynamics in a Wright-Fisher process

Abstract: Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of offspring. The total population size is constant. The resulting Markov process has two absorbing states corresponding to homogeneous populations of all A or all B. We quantify frequency dependent selection by comparing the absorption probabilities to the corresponding probabilities under random drift. We derive conditions for selection to favor one strategy or the other by using the concept of total positivity. In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3.

Economic comparability of information systems.

Abstract: An information system is a set of potential messages to be received by the decision maker. It is characterized by the statistical relation of the messages to the payoff-relevant events, and also by the message cost.1 Neglecting this cost, the (gross) value of an information system for a given user is the (gross) payoff that he would obtain, on the average, if he would respond to each message by the most appropriate decision. Thus (gross) information value depends not only on the statistical relation between messages and events but also on the payoff function. The latter expresses the user’s ‘tastes’ and ‘technology’. The ordering of statistically defined information systems by their values is therefore at most a partial one. This contrasts with the complete ordering of information systems (channels) by their equivocation (a statistical parameter used in the classical information theory that disregards variation of payoff functions from user to user).

Economic games on the internet: the effect of $1 stakes.

Abstract: Online labor markets such as Amazon Mechanical Turk (MTurk) offer an unprecedented opportunity to run economic game experiments quickly and inexpensively. Using Mturk, we recruited 756 subjects and examined their behavior in four canonical economic games, with two payoff conditions each: a stakes condition, in which subjects' earnings were based on the outcome of the game (maximum earnings of $1); and a no-stakes condition, in which subjects' earnings are unaffected by the outcome of the game. Our results demonstrate that economic game experiments run on MTurk are comparable to those run in laboratory settings, even when using very low stakes.

Finite rationality and interpersonal complexity in repeated games

Abstract: A measure of complexity for repeated game strategies is studied. This measure facilitates the investigation of some issues regarding finite rationality and the structure of subgame perfect equilibria of repeated games with discounting. Specifically, the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set, i.e., the number of distinct strategies induced by the original strategy in all possible subgames. We observe that this cardinality is equal to the size (cardinality of the state set) of the smallest automaton which can implement the strategy. Thus, in a sense, complexity is measured on the basis of the amount of computing power inherent in the strategy. A measure of strategic memory is also studied. The following results are obtained: (1) combining two notions of "bounded rationality" (epsilon equilibrium and finite complexity), we find that every subgame perfect equilibrium of the repeated game can be approximated (with regard to payoffs) by a subgame perfect epsilon equilibrium of finite complexity. (2) For a generic class of normal form stage games, at every discount robust subgame perfect (DRSP) equilibrium, there are necessary relationships among the complexities and memories of the players' strategies. In the two player case, strategies must be equally complex and must have equal memories. (3) For a second class of two pla-yer stage games, we show that the payoff vectors for all DRSP equilibria are obtainable via equilibria in which the players' strategies are equally complex and have equal memoiies.

Evolutionary Dynamics in Set Structured Populations

Abstract: Evolutionary dynamics are strongly affected by population structure. The outcome of an evolutionary process in a well-mixed population can be very different from that in a structured population. We introduce a powerful method to study dynamical population structure: evolutionary set theory. The individuals of a population are distributed over sets. Individuals interact with others who are in the same set. Any 2 individuals can have several sets in common. Some sets can be empty, whereas others have many members. Interactions occur in terms of an evolutionary game. The payoff of the game is interpreted as fitness. Both the strategy and the set memberships change under evolutionary updating. Therefore, the population structure itself is a consequence of evolutionary dynamics. We construct a general mathematical approach for studying any evolutionary game in set structured populations. As a particular example, we study the evolution of cooperation and derive precise conditions for cooperators to be selected over defectors.