arXiv subjects

Hanping Xu

Publications and source records attributed to Hanping Xu.

6 recordsLinked to original sources

arXiv2026

Weak Atomic Continuity and Subgame Perfection

Subgame-perfect equilibrium need not exist in continuous games with perfect information when Nature moves. Under standard regularity assumptions, we prove that weak atomic continuity of Nature's transition probabilities yields a measurable pure-strategy subgame-perfect equilibrium for finite and infinite horizons. The condition, originating in the population genetics literature, is necessary for the existence of subgame-perfect equilibrium uniformly over the remaining primitives: whenever this condition is violated, one can construct a dynamic game with no subgame-perfect equilibrium, even in behavioral strategies. The proof preserves compactness and upper hemicontinuity of continuation payoff correspondences under integration without requiring convexity.

econ.TH↗

arXiv2026

Universal Nonexistence of Monotone Equilibrium in Multiunit Auctions with Risk Aversion

We establish universal nonexistence results for monotone pure-strategy equilibrium in multiunit auctions with risk-averse bidders. Fix any number of bidders greater than one and any profile of strictly increasing concave utilities, with at least one strictly risk-averse bidder. Under uniform pricing, for every supply of at least three units, we construct independent, full-support type distributions under which neither lowest-winning-bid nor highest-losing-bid pricing admits an admissible monotone equilibrium. Under discriminatory pricing, we construct a finite supply and independent, full-support type distributions that preclude monotone pure-strategy equilibrium. We extend these results to all-pay auctions and finite bid grids.

econ.TH↗

arXiv2026

Extremal Perfect Monotone Equilibria in Bayesian Games with Strategic Complementarities

We study sharp bounds on equilibrium behavior in Bayesian games when players may make mistakes. Under strategic complementarities, the set of behavioral perfect equilibria has a largest and a smallest element, both in pure strategies. We ask when these bounds are monotone and how they depend on the way mistakes are made. For monotone supermodular games, we consider limits of equilibria under increasing perturbations, in the sense that conditional tremble distributions have full support and increase stochastically with type. We show that the largest and smallest perfect equilibria exist, which are pure and monotone. Under the general perfection notion, the extremal perfect equilibria continue to be monotone in the setting with finite actions. With infinite actions, the extremal perfect equilibria can be nonmonotone, and the set of perfect monotone equilibria can even lack extrema.

econ.TH↗

arXiv2026

Monotone Equilibrium, Admissibility and Perfection

This paper studies monotone equilibrium, admissibility, and perfection in Bayesian games. Athey (2001), McAdams (2003), and Reny (2011) prove existence of pure-strategy monotone equilibria under single-crossing and quasi-supermodularity. We construct a counterexample satisfying these assumptions but with no admissible monotone equilibrium, showing these results cannot generally be strengthened without further conditions. To address this existence problem, we introduce perfect monotone equilibrium, combining monotonicity with trembling-hand robustness. We show that stronger assumptions such as increasing differences and supermodularity ensure existence of perfect (and hence admissible) monotone equilibria. We also demonstrate the practical relevance of our results through auctions and Bertrand competitions.

econ.TH↗

arXiv2024

Equilibrium convergence in large games

This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of fiinite-player games, the limit of any convergent sequence of Nash equilibria of the corresponding finite-player games can be induced by a Nash equilibrium of the large game. Such a result goes beyond earlier results on the closed graph property for pure strategy Nash equilibrium correspondence in large games in multiple aspects. An application on equilibrium selection in large games is also presented.

math.OC↗

arXiv2019

Does randomization matter in dynamic games?

This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every two-player dynamic zero-sum game with nature has the no-mixing property, which implies that mixed strategy is useless in this most classical class of games. As for applications, we show the existence of pure-strategy subgame-perfect equilibria in two-player zero-sum games with nature. Based on the main result, we also prove the existence of a universal subgame-perfect equilibrium that can induce all the pure-strategy subgame-perfect equilibria in such games. A generalization of the main result for multiple players and some further results are also discussed.

math.OC↗