The Splitting Game: Value and Optimal Strategies

Miquel Oliu-Barton ()
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Miquel Oliu-Barton: Université Paris-Dauphine, PSL Research University, CNRS, CEREMADE

Dynamic Games and Applications, 2018, vol. 8, issue 1, No 8, 157-179

Abstract: Abstract 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.

Keywords: Splitting game; Games with incomplete information; Stochastic games; Mertens–Zamir system; Uniform value; State-independent signaling (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13235-017-0216-8

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