5,692 research outputs found
Computer Science and Game Theory: A Brief Survey
There has been a remarkable increase in work at the interface of computer
science and game theory in the past decade. In this article I survey some of
the main themes of work in the area, with a focus on the work in computer
science. Given the length constraints, I make no attempt at being
comprehensive, especially since other surveys are also available, and a
comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic
Axiomatic Approach to Solutions of Games
We consider solutions of normal form games that are invariant under strategic
equivalence. We consider additional properties that can be expected (or be
desired) from a solution of a game, and we observe the following:
- Even the weakest notion of individual rationality restricts the set of
solutions to be equilibria. This observation holds for all types of solutions:
in pure-strategies, in mixed strategies, and in correlated strategies where the
corresponding notions of equilibria are pure-Nash, Nash and coarse-correlated.
An action profile is (strict) simultaneous maximizer if it simultaneously
globally (strictly) maximizes the payoffs of all players.
- If we require that a simultaneous maximizer (if it exists) will be a
solution, then the solution contains the set of pure Nash equilibria.
- There is no solution for which a strict simultaneous maximizer (if it
exists) is the unique solution
Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms.
We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses or bestresponses. First, we show that a necessary condition for recurrent implementation in better-response dynamics (BRD) is a small variation of Maskin monotonicity, which we call quasimonotonicity. We also provide a mechanism for implementation in BRD if the rule is quasimonotonic and excludes worst alternatives – no worst alternative (NWA). Quasimonotonicity and NWA are both necessary and sufficient for absorbing implementation in BRD. Moreover, they characterize implementation in strict Nash equilibria. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for recurrent implementation in interim BRD. Both conditions are also essentially sufficient for recurrent implementation, together with a Bayesian NWA. A characterization of implementation in strict Bayesian equilibria is also provided. Partial implementation results are also obtained.Robust implementation; Bounded rationality; Evolutionary dynamics; Mechanisms;
On the robustness of learning in games with stochastically perturbed payoff observations
Motivated by the scarcity of accurate payoff feedback in practical
applications of game theory, we examine a class of learning dynamics where
players adjust their choices based on past payoff observations that are subject
to noise and random disturbances. First, in the single-player case
(corresponding to an agent trying to adapt to an arbitrarily changing
environment), we show that the stochastic dynamics under study lead to no
regret almost surely, irrespective of the noise level in the player's
observations. In the multi-player case, we find that dominated strategies
become extinct and we show that strict Nash equilibria are stochastically
stable and attracting; conversely, if a state is stable or attracting with
positive probability, then it is a Nash equilibrium. Finally, we provide an
averaging principle for 2-player games, and we show that in zero-sum games with
an interior equilibrium, time averages converge to Nash equilibrium for any
noise level.Comment: 36 pages, 4 figure
The minority game: An economics perspective
This paper gives a critical account of the minority game literature. The
minority game is a simple congestion game: players need to choose between two
options, and those who have selected the option chosen by the minority win. The
learning model proposed in this literature seems to differ markedly from the
learning models commonly used in economics. We relate the learning model from
the minority game literature to standard game-theoretic learning models, and
show that in fact it shares many features with these models. However, the
predictions of the learning model differ considerably from the predictions of
most other learning models. We discuss the main predictions of the learning
model proposed in the minority game literature, and compare these to
experimental findings on congestion games.Comment: 30 pages, 4 figure
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