The testable implications of zero-sum games

Abstract

We study Nash-rationalizable joint choice behavior under restriction on zerosum games. We show that interchangeability of choice behavior is the only additional condition which distinguishes zero-sum games from general noncooperative games with respect to testable implications. This observation implies that in some sense interchangeability is not only a necessary but also a sufficient property which differentiates zero-sum games.

The empirical implications of rank in Bimatrix games

“…More recently, there are two other papers that study noncooperative games via the revealedpreference approach, [12,16]. Like us, [12] does not require observed choices in all possible subgames.…”

“…Our results imply that this hardness only arises when the sets of strategies are non-laminar. More related to our work is [16], which also studies zero-sum games from the revealed-preference perspective. However, [16] has the same restrictions as [21], i.e., all possible subsets of strategies are observed.…”

“…More related to our work is [16], which also studies zero-sum games from the revealed-preference perspective. However, [16] has the same restrictions as [21], i.e., all possible subsets of strategies are observed. In this setup, [16] proves that zero-sum has a very particular empirical implication (on top of the ones imposed by Nash rationalizability): the well-known property of exchangeability of Nash equilibria of zero-sum games.…”

Every Choice Function Is Backwards-Induction Rationalizable

“…They identify necessary and sufficient conditions under which there exist n preferences over the conceivable joint actions such that the joint actions selected from each subgame form coincide with the Nash equilibria of the corresponding subgame. Lee (2012) characterizes choice behavior that is rationalizable via Nash equilibria of zero-sum games.…”

“…They identified necessary and sufficient conditions under which there exist n preferences over the conceivable joint actions such that the joint actions selected from each subgame form coincide with the Nash equilibria of the corresponding subgame. Demuynck and Lauwers (2009) extended the analysis to mixed strategies while Lee (2012) characterized choice behavior that is rationalizable via Nash equilibria of zero-sum games. Ray and Zhou (2001) fixed a finite-length game tree and an assignment of the decision nodes to a given set of n agents.…”