Diagonal Payoff Security and Equilibrium Existence in Quasi-Symmetric Discontinuous Games

Corrigendum to “On the Existence of Pure and Mixed Strategy Nash Equilibrium in Discontinuous Games”

“…© 2022 The Econometric Society https://doi.org/10.3982/ECTA20900 o2 C. EWERHART AND P. J. RENY strategy Nash equilibrium. This game is due to Ewerhart (2022). Consider the two-person game on the unit square in which a player's payoff, u(x y), when he chooses x, is x if the other player chooses y < 1/2 but is 1 − x if the other player chooses y ≥ 1/2.…”

“…To see that the missing “ y 's” in the original definition of diagonal payoff security given in Reny (1999) are needed, we exhibit a game, let us call it , that satisfies the (pre‐correction) hypotheses of Reny's Corollary 4.3 but does not possess a symmetric pure strategy Nash equilibrium. This game is due to Ewerhart (2022). Consider the two‐person game on the unit square in which a player's payoff, , when he chooses x , is x if the other player chooses but is if the other player chooses .…”

“…This corrected definition is in fact the definition originally given in Reny (1996), which was the initial submission to Econometrica for Reny (1999). 3 Ewerhart (2022) points out the error in Reny (1999) and independently provides the correction 4…”

“…44 Ewerhart (2022) uses the term “ strong diagonal payoff security” for the corrected definition. We drop “strong” here. …”