The Splitting Game: Value and Optimal Strategies
Oliu-Barton, Miquel (2018), The Splitting Game: Value and Optimal Strategies, Dynamic Games and Applications, 8, 1, p. 157-179. 10.1007/s13235-017-0216-8
TypeArticle accepté pour publication ou publié
Journal nameDynamic Games and Applications
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We introduce the dependent splitting game, a zero-sum stochastic game in which the players jointly control a martingale. This game models the transmission of information in repeated games with incomplete information on both sides, in the dependent case: The state variable represents the martingale of posterior beliefs. We establish the existence of the value for any fixed, general evaluation of the stage payoffs, as a function of the initial state. We then prove the convergence of the value functions, as the evaluation vanishes, to the unique solution of the Mertens–Zamir system of equations is established. From this result, we derive the convergence of the values of repeated games with incomplete information on both sides, in the dependent case, to the same function, as the evaluation vanishes. Finally, we establish a surprising result: Unlike repeated games with incomplete information on both sides, the splitting game has a uniform value. Moreover, we exhibit a couple of optimal stationary strategies for which the stage payoff and the state remain constant.
Subjects / KeywordsSplitting game; Games with incomplete information; Stochastic games; Mertens–Zamir system; Uniform value; State-independent signaling
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