International Journal of Game Theory

Lahkar, Ratul; Mahanta, Amarjyoti

doi: 10.1007/s00182-025-00942-6pmid: N/A

In the ultimatum minigame, proposers can offer either half the total prize or a minimal quantity (e.g., 1). Responders can accept or reject. At the subgame perfect equilibrium, proposers offer the minimal quantity and responders accept. We apply the best experienced payoff (BEP) dynamic to the large population version of this game. The BEP dynamic is generated when players try their strategies a certain number of times and choose the strategy that generates the highest average payoff. We establish conditions under which the subgame perfect equilibrium is stable or unstable. If it is unstable, another stable state can arise where a significant fraction of proposers make high offers.

Rachmilevitch, Shiran

doi: 10.1007/s00182-025-00941-7pmid: N/A

I consider Nash’s demand game (NDG) in the context of resource-allocation, rather than in the abstract utility space. If the resource is one-dimensional, the known results from the NDG literature are recovered: either the Nash solution is uniquely supported at the perturbations’ limit, or the entire (relative interior of the) Pareto frontier is supported; which case obtains depends on the type of perturbation. I show that, contrary to the prominence of the Nash solution under smoothing in the utility space, the entire frontier can be supported under a variety of economically-plausible perturbations. The case where the resource is multi-dimensional is qualitatively different.

Lipman, Barton L.

doi: 10.1007/s00182-025-00935-5pmid: N/A

I don’t know.

Carmona, Guilherme; Podczeck, Konrad

doi: 10.1007/s00182-025-00932-8pmid: N/A

We consider Bayes–Nash equilibria of large semi-anonymous games (i.e., each player’s payoff is determined by his type, his action, and the distribution of the realized types and choices of the others). In a model with finite type and action spaces, we provide a characterization of limits of sequences of Bayes-Nash equilibria as the number of players goes to infinity. Based on this, we show that strict pure-strategy Bayes–Nash equilibria exist in all sufficiently large finite-player games for generic distributions of players’ payoff functions and type distributions.

Li, Longjian; Toda, Alexis Akira

doi: 10.1007/s00182-025-00922-wpmid: N/A

We study a game between N job applicants who incur a cost c∈[0,1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$c\in [0,1)$$\end{document} (relative to the job value) to reveal their type during interviews and an administrator who seeks to maximize the probability of hiring the best applicant. We define a full learning equilibrium and prove its existence, uniqueness, and optimality. In full learning equilibrium, the administrator accepts the current best applicant n with probability c if n<n∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n<n^*$$\end{document} and with probability 1 if n≥n∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n\ge n^*$$\end{document} for a threshold n∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n^*$$\end{document} independent of c. In contrast to the case without cost, where the success probability converges to 1/e≈0.37\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$1/\textrm{e}\approx 0.37$$\end{document} as N tends to infinity, with cost the success probability decays like N-c\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N^{-c}$$\end{document}.

Anno, Hidekazu

doi: 10.1007/s00182-025-00937-3pmid: N/A

We consider the problem of stochastically allocating n indivisible objects to n agents when each agent assigns cardinal utility values to the objects. In this context, Zhou (1990) demonstrates Gale’s conjecture in a stronger form: No rule is strategy-proof, ex ante efficient, and symmetric. We further strengthen this impossibility theorem by relaxing the requirement of symmetry. Consequently, we indicate that every strategy-proof and ex ante efficient rule satisfies neither symmetry nor the equal division lower bound.

Khubulashvili, Robizon

doi: 10.1007/s00182-025-00944-4pmid: N/A

I explore the dynamics of collaboration under incomplete information, focusing on the tension between the benefits and costs of collaboration. Specifically, I examine the case of two agents: one is an incumbent with well-known ability, and the other is an entrant with unobservable ability. If the incumbent’s incentive to free ride depends on the entrant’s possible types and learns the collaborator’s type based on history, then accumulating the reputation of being a high-ability type will lead to a breakup of the partnership. The breakup occurs because the incumbent’s incentive to free ride increases if the entrant accumulates a high enough reputation. I design an experiment to study the incumbent’s incentives to free ride after observing different paths of the entrant’s reputation building. As predicted by theory, I find that reputation-building might hinder collaboration.

Hofbauer, Josef; Pawlowitsch, Christina

doi: 10.1007/s00182-025-00927-5pmid: N/A

The theory of costly signaling (Spence in Q J Econ 87:355–374, 1973) is a well-established paradigm in economics and theoretical biology, where it is also known as the Handicap Principle (Zahavi J Theor Biol 53:205–214, 1975). Nevertheless, while costly-signaling games have been extensively studied in classical game theory (focused on Nash equilibrium and its refinements), evolutionary dynamics in costly-signaling games are relatively unexplored. This paper gives a comprehensive account of evolutionary dynamics in two canonical classes of games with two states of nature, two signals, and two possible reactions to signals: a model with differential signaling costs (similar to Spence’s model) and a model with differential benefits from success (similar to Milgrom and Roberts’s in J Polit Econ 94:796–821, 1986, respectively Grafen’s J Theor Biol 144:517–546, 1990, model). We first use index theory to give a necessary condition for the dynamic stability of the equilibria in these games. Then, we study the replicator dynamics and the best-response dynamics. Along the way, we relate our findings to classical equilibrium refinements that test for the plausibility of beliefs off the equilibrium path.

Ismail, Mehmet S.; Peeters, Ronald

doi: 10.1007/s00182-025-00938-2pmid: N/A

This paper contributes to the literature on pure equilibria in symmetric zero-sum games in two main ways. First, we introduce new sufficient conditions, including interchangeability and weak quasiconcavity, for the existence of such equilibria. Second, we uncover relationships between these newly introduced conditions and existing ones. For instance, we demonstrate that the class of weakly quasiconcave games generalizes the class of quasiconcave games and ordinal potential games. Additionally, we show that exact potential games satisfy the interchangeability condition. However, no logical relationship exists between interchangeability and (weak) quasiconcavity.

Falniowski, Fryderyk; Mertikopoulos, Panayotis

doi: 10.1007/s00182-025-00929-3pmid: N/A

We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential/multiplicative weights algorithm for online learning. Even though these models share the same continuous-time limit—the replicator dynamics—we show that second-order effects play a crucial role and may lead to drastically different behaviors in each model, even in very simple, symmetric 2×2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2\times 2$$\end{document} games. Specifically, we study the resulting discrete-time dynamics in a class of parametrized congestion games, and we show that (i) in the biological model of intra-species competition, the dynamics remain convergent for any parameter value; (ii) the dynamics of pairwise proportional imitation exhibit an entire range of behaviors for larger time steps and different equilibrium configurations (stability, instability, and even Li–Yorke chaos); while (iii) in the exponential/multiplicative weights algorithm, increasing the time step (almost) inevitably leads to chaos (again, in the formal, Li–Yorke sense). This divergence of behaviors comes in stark contrast to the globally convergent behavior of the replicator dynamics, and serves to delineate the extent to which the replicator dynamics provide a useful predictor for the long-run behavior of their discrete-time origins.