Download Repeated Games and Reputations: Long-Run Relationships by George J. Mailath, Larry Samuelson PDF

By George J. Mailath, Larry Samuelson

Custom-made and carrying on with relationships play a significant function in any society. Economists have equipped upon the theories of repeated video games and reputations to make vital advances in realizing such relationships. Repeated video games and Reputations starts with a cautious improvement of the basic ideas in those theories, together with the notions of a repeated online game, procedure, and equilibrium. Mailath and Samuelson then current the vintage folks theorem and acceptance effects for video games of ideal and imperfect public tracking, with the advantage of the fashionable analytical instruments of decomposability and self-generation. additionally they current more moderen advancements, together with effects past folks theorems and up to date paintings in video games of non-public tracking and replacement methods to reputations. Repeated video games and Reputations synthesizes and unifies the titanic physique of labor during this region, bringing the reader to the study frontier. distinct arguments and proofs are given all through, interwoven with examples, discussions of ways the idea is for use within the research of relationships, and financial purposes. The ebook may be valuable to these doing easy study within the concept of repeated video games and reputations in addition to these utilizing those instruments in additional utilized study.

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Sample text

Note that although every state in W is accessible from wEE , the state wEE is not accessible from wSS . ● The advantage of the automaton representation is that we need only verify the strategy profile induced by (W , w, f, τ ) is a Nash equilibrium, for each w ∈ W , to confirm that the strategy profile induced by (W , w0 , f, τ ) is a subgame-perfect equilibrium. 2 (and its proof omitted). 1 perfect equilibrium if and only if, for all w ∈ W accessible from w0 , the strategy profile induced by (W , w, f, τ ) is a Nash equilibrium of the repeated game.

This arrangement capitalizes on the differences in the two players’ discount factors, with the impatient player 2 essentially borrowing payoffs from the more patient player 1 in early periods to be repaid in later periods, to expand the set of feasible repeated-game payoffs beyond those of the stage game. Lehrer and Pauzner (1999) examine repeated games with differing discount factors. 2 i and strategies σi , Ui (σ ) ≥ Ui (σi , σ−i ). 2 on minmax utilities: p Lemma If σ is a pure-strategy Nash equilibrium, then for all i, Ui (σ ) ≥ vi .

T − 1 and (T , R) to be played in subsequent periods yields a repeated game vector outside the convex hull of {(3, 1), (0, 0), (1, 3)}, being in particular above the line segment joining payoffs (3, 1) and (1, 3). This outcome averages over the payoffs (3, 1) and (1, 3), but places relatively high player 2 payoffs in early periods and relatively high player 1 payoffs in later periods, giving repeated-game payoffs to the two players of player 1 : and player 2 : (1 − δ1T ) + 3δ1T 3(1 − δ2T ) + δ2T .

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