This paper considers a version of Bush and Mosteller's ([5], [6]) stochastic learning theory in the context of games. We compare this model of learning to a model of biological evolution. The purpose is to investigate analogies between learning and evolution. We¯nd that in the continuous time limit the biological model coincides with the deterministic, continuous time replicator process. We give conditions under which the same is true for the learning model. For the case that these conditions do not hold, we show that the replicator process continues to play an important role in characterising the continuous time limit of the learning model, but that a di®erent e®ect (\Probability Matching") enters as well.
What are good voting rules if voting is costly? We analyze this question for the case that an electorate chooses among two alternatives. In a symmetric private value model of voting we show that majority voting with voluntary participation Paretodominates majority voting with compulsory participation as well as random decision-making.
What is the best way to auction an asset? How should a group of people organize themselves to ensure the best provision of public goods? How should exchanges be organized? This book addresses these questions and more through an exploration of the economic theory of mechanism design. Mechanism design is reverse game theory. Whereas game theory takes the rules of the game as a given and makes predictions about the behavior of strategic players, the theory of mechanism design goes a step further and selects the optimal rules of the game. A relatively new economic theory, mechanism design studies the instrument itself as well as the results of the instrument. This book provides explanations of classic results in the theory of mechanism design, such as Myerson's theorem on expected revenue maximizing auctions, Myerson and Satterthwaite's theorem on the impossibility of ex post efficient bilateral trade with asymmetric information, and Gibbard and Satterthwaite's theorem on the non-existence of dominant strategy voting mechanisms. It also provides an examination of the frontiers of current research in the area.
This article considers a simple model of reinforcement learning. All behavior change derives from the reinforcing or deterring effect of instantaneous payoff experiences. Payoff experiences are reinforcing or deterring depending on whether the payoff exceeds an aspiration level or falls short of it. Over time, the aspiration level is adjusted toward the actually experienced payoffs. This article shows that aspiration level adjustments may improve the decision maker's long-run performance by preventing him or her from feeling dissatisfied with even the best available strategies. However, such movements also lead to persistent deviations from expected payoff maximization by creating "probability matching" effects.
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