The punctuality stability of the Nash equilibrium: the advantage of a late player in potential and aggregative games

Operational Research. 2026. Vol. 1. No. 2. P. 1–23.

Gusev V.

In a Nash equilibrium, no player can gain by unilaterally deviating. In many practical settings, however, players can also choose when to act, and delaying may be profitable because it allows a player to move last and respond to others (for example, waiting for competitors to announce prices before setting one’s own). We ask whether one can select a Nash equilibrium in which no player has an incentive to delay intentionally. To address this, we introduce punctually stable Nash-equilibrium, that is, a Nash equilibrium with the additional property that intentional tardiness is not advantageous. We study existence of punctually stable Nash-equilibria in potential games and aggregative games. Remarkably, in some environments, all-player punctuality can be achieved without explicitly penalizing late arrivals.

Keywords: Nash equilibrium, равновесие по Нэшу, potential games, потенциальные игры, punctuality stability, aggregative games, пунктуальная устойчивость, агрегированные игры

Publication based on the results of: Economic and mathematical analysis of markets, games, and decision-making (2025)