Download PDF by George J. Mailath, Larry Samuelson: Repeated games and reputations - long-run relationships

By George J. Mailath, Larry Samuelson

ISBN-10: 0195300793

ISBN-13: 9780195300796

Custom-made and carrying on with relationships play a principal position in any society. Economists have outfitted upon the theories of repeated video games and reputations to make very important advances in figuring out such relationships. Repeated video games and Reputations starts with a cautious improvement of the elemental techniques in those theories, together with the notions of a repeated online game, method, and equilibrium. Mailath and Samuelson then current the vintage people theorem and attractiveness effects for video games of ideal and imperfect public tracking, with the advantage of the fashionable analytical instruments of decomposability and self-generation. in addition 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 techniques to reputations. Repeated video games and Reputations synthesizes and unifies the mammoth physique of labor during this quarter, bringing the reader to the examine frontier. particular arguments and proofs are given all through, interwoven with examples, discussions of the way the idea is for use within the learn of relationships, and fiscal functions. The publication may be beneficial to these doing simple learn within the concept of repeated video games and reputations in addition to these utilizing those instruments in additional utilized examine.

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2) t=0 As usual, the payoff to player i from a profile of mixed or behavior strategies σ is the expected value of the payoffs of the realized outcomes, also denoted Ui (σ ). 2) (and throughout) by the factor (1 − δ). This ensures that U (σ ) = (U1 (σ ), . . , Un (σ )) ∈ F † for all repeated-game strategy profiles σ . We can then readily compare payoffs in the repeated game and the stage game, and compare repeated-game payoffs for different (common) discount factors. 3 t-period history is a list of t action profiles and t realizations of the public correlating device, (ω0 , a 0 ; ω1 , a 1 ; .

N}. 2 Public Correlation It is sometimes natural to allow players to use a public correlating device. Such a device captures a variety of public events that players might use to coordinate their actions. 5 3. Allowing player i to mix will not change i’s minmax payoff, because every action in the support of a mixed best reply is also a best reply for player i. 4. We denote the mixture that assigns probability αi (ai ) to action ai by ai αi (ai ) ◦ ai . 5. A small body of literature has studied this case.

Some of the payoffs that are in F † but not F can be obtained via independent mixtures, ignoring the correlating device, over the sets {T , B} and {L, R}. For example, F † contains (20/9, 20/9), obtained by independent mixtures that place probability 2/3 on T (or L) and 1/3 on B (or R). A pure strategy that uses the public correlation device to place probability 4/9 on (T , L), 2/9 on each of (T , R) and (B, L), and 1/9 on (B, R) achieves the same payoff. 1 ■ 19 The Canonical Repeated Game mixtures.

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Repeated games and reputations - long-run relationships by George J. Mailath, Larry Samuelson

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