Determinacy of equilibrium outcome distributions for zero sum and common utility games

Abstract

a b s t r a c tWe show the generic finiteness of probability distributions induced on outcomes by the Nash equilibria in two player zero sum and common interest outcome games.

Generic finiteness of equilibrium distributions for bimatrix outcome game forms

“…Govindan and McLennan (2001) proved that for games with two outcomes and any number of players the number of equilibrium distributions on outcomes is generically finite. Similar results have been obtained for two player, three outcomes games (González-Pimienta 2010), sender-receiver cheap-talk games (Park 1997), zero sum or common interest games (Govindan andMcLennan 1998, Litan andMarhuenda 2012) and games with three players and two strategies each (Litan, Marhuenda, and Sudhölter 2015).…”

“…We follow very closely the notation and set up adopted in Litan, Marhuenda, and Sudhölter (2015) and Litan and Marhuenda (2012). Let S 1 = {1, 2, .…”

“…The case k 1 = k 2 = k of the Proposition is a standard result in elementary Linear Algebra. See Lemmas 3.2, 3.3 and 3.4 in Litan and Marhuenda (2012) for the proof of parts (b) and (c).…”

“…The proof is based on techniques developed in Litan and Marhuenda (2012). A review of these and the details of the proof are provided in the appendix.…”

Generic Finiteness of Equilibrium Distributions for Bimatrix Outcome Game Forms

“…The following is proved in Lemmas 3.3 and 3.4 of Litan and Marhuenda (2012). For V ⊂ R l a linear subspace and a ∈ R l we let aV = V a = {a · v : v ∈ V }.…”