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on Game Theory |
| By: | Josue Ortega |
| Abstract: | We analyze the performance of the Boston mechanism under equilibrium play in uniform random markets. We provide two results. First, while the share of students assigned to their first preference is 63% under truthfulness, this fraction becomes vanishingly small in any Nash equilibrium of the preference revelation game induced by the Boston mechanism. Second, we show that there is a Nash equilibrium of the corresponding preference revelation game where the average student is assigned to a highly undesirable school-dramatically worse ranked than the logarithmic rank achieved under truthfulness. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.19450 |
| By: | Fang-Fang Tang; Yongsheng Xu |
| Abstract: | A player's payoff is modeled as consisting of two parts: a rational-value part and a distortion-value part. It is argued that the (total) payoff function should be used to explain and predict the behaviors of the players, while the rational value function should be used to conduct welfare analysis of the final outcome. We use the Nash demand game to illustrate our model. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.16465 |
| By: | Fang-Fang Tang; Yongsheng Xu |
| Abstract: | A distortion function, which captures the payoff gap between a player's actual payoff and her true payoff, is introduced and used to analyze games. In our proposed framework, we argue that players' actual payoff functions should be used to explain and predict their behaviors, while their true payoff functions should be used to conduct welfare analysis of the outcomes. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.16467 |
| By: | Sylvain Béal (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France); Léa Munich (Université Paris Panthéon Assas, CRED UR 7321, F-75005 Paris, France); Philippe Solal (Université Paris Panthéon Assas, GATE Lyon Saint-Etienne, UMR 5824, F-42023 Saint-Etienne, France); Kevin Techer (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France) |
| Abstract: | We consider cooperative TU-games with unpaid players, which are described by a TUgame and two categories of players, paid and unpaid. Unpaid players participate in the cooperative game but are not rewarded for their participation, for instance for legal reasons. The objective is then to determine how the contributions of unpaid players are redistributed among the paid players. To meet this goal, we introduce and characterize axiomatically three values that are inspired by the Shapley value but differ in the way they redistribute the contributions of unpaid players. These values are unified as instances of a more general two-step allocation procedure. |
| Keywords: | Unpaid players, Shapley value, Harsanyi dividends, axioms, two-step procedure, Priority value |
| JEL: | C72 |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:crb:wpaper:2025-11 |
| By: | Dianetti, Jodi (Center for Mathematical Economics, Bielefeld University); Nendel, Max (Center for Mathematical Economics, Bielefeld University); Tangpi, Ludovic (Center for Mathematical Economics, Bielefeld University); Wang, Shichun (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the propagation of the Lasry-Lions monotonicity to the optimal equilibrium value, as a function of the realization of the initial condition and its distribution. Secondly, we prove a pasting property for equilibria; that is, we construct equilibria to multi-period discrete-time mean field games by recursively pasting the equilibria of suitably initialized single- period games. Then, we show that any sequence of equilibria of discrete-time mean field games with discretized noise converges (up to a subsequence) to some equilibrium of the continuous-time mean field game as the mesh size of the discretization tends to zero. When the cost functions of the game satisfy the Lasry-Lions monotonicity property, we strengthen this convergence result by providing a sharp convergence rate. |
| Date: | 2025–08–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:743 |
| By: | Steg, Jan-Henrik (Center for Mathematical Economics, Bielefeld University); Garashli, Elshan (Center for Mathematical Economics, Bielefeld University); Greinecker, Michael (Center for Mathematical Economics, Bielefeld University); Kuzmics, Christoph (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | For cheap-talk games with a binary state space in which the sender has state-independent preferences, we characterize equilibria that are robust to introducing slight state-dependence on the side of the sender. Not all equilibria are robust, but the sender-optimum is always achieved at some robust equilibrium. |
| Keywords: | Cheap talk, Communication, Information transmission, Robustness |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:727 |
| By: | Brendon G. Anderson |
| Abstract: | In this paper, we consider finite-strategy approximations of infinite-strategy evolutionary games. We prove that such approximations converge to the true dynamics over finite-time intervals, under mild regularity conditions which are satisfied by classical examples, e.g., the replicator dynamics. We identify and formalize novel characteristics in evolutionary games: choice mobility, and its complement choice paralysis. Choice mobility is shown to be a key sufficient condition for the long-time limiting behavior of finite-strategy approximations to coincide with that of the true infinite-strategy game. An illustrative example is constructed to showcase how choice paralysis may lead to the infinite-strategy game getting "stuck, " even though every finite approximation converges to equilibrium. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.10567 |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics); Elena Parilina (Saint Peterburg State University); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne, CNRS, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics); Georges Zaccour (GERAD, HEC Montréal) |
| Abstract: | Dealing with climate change requires that all countries engage in costly efforts to reduce their emissions. Reaching this objective has so far been elusive because it is in the best interest of each country to let the others do the effort and benefit itself from a better environment. The presence of negative externalities and strategic behavior have made game theory a natural paradigm to design an international environmental agreement (IEA) that codifies what countries should do. Considering that countries are sovereign and no supranational entity can impose an agreement, a stream of literature adopted a noncooperative mode of play to the formation of an environmental coalition. On the other hand, as joint optimization of all countries’ payoff leads to the best outcome, cooperative games approach has also been proposed to share the cost of climate change. Both approaches have their pros and cons. In this paper, we propose a model of coalition formation that combines both cooperative and noncooperative modes of play. Starting from any given coalition, we implement a Markov process that shows sequentially which countries join or leave the coalition until reaching an absorbing state. All possible sequential scenarios are considered and an allocation to the player is made taking into account individual rationality. An illustration with vulnerable and invulnerable countries to pollution is given |
| Keywords: | Coalition Formation; International Environmental Agreement; Markov Process; Shapley Value |
| JEL: | C71 C72 F53 Q53 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:mse:cesdoc:25020 |
| By: | Dammann, Felix (Center for Mathematical Economics, Bielefeld University); Rodosthenous, Neofytos (Center for Mathematical Economics, Bielefeld University); Villeneuve, Stéphane (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We introduce a non-zero-sum game between a government and a legislative body to study the optimal level of debt. Each player, with different time preferences, can intervene on the stochastic dynamics of the debt-to-GDP ratio via singular stochastic controls, in view of minimiz- ing non-continuously differentiable running costs. We completely characterise Nash equilibria in the class of Skorokhod-reflection-type policies. We highlight the importance of different time preferences resulting in qualitatively different type of equilibria. In particular, we show that, while it is always optimal for the government to devise an appropriate debt issuance policy, the legislator should opti- mally impose a debt ceiling only under relatively low discount rates and a laissez-faire policy can be optimal for high values of the legislator’s discount rate. |
| Keywords: | We introduce a non-zero-sum game between a government and a legislative body to study the optimal level of debt. Each player, with different time preferences, can intervene on the stochastic dynamics of the debt-to-GDP ratio via singular stochastic controls, in view of minimiz- ing non-continuously differentiable running costs. We completely characterise Nash equilibria in the class of Skorokhod-reflection-type policies. We highlight the importance of different time preferences resulting in qualitatively different type of equilibria. In particular, we show that, while it is always optimal for the government to devise an appropriate debt issuance policy, the legislator should opti- mally impose a debt ceiling only under relatively low discount rates and a laissez-faire policy can be optimal for high values of the legislator’s discount rate |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:730 |
| By: | Noemí Navarro (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, UR - Université de Rennes); Róbert Veszteg (Waseda University [Tokyo, Japan]) |
| Abstract: | We experimentally test welfarism and scale invariance, two prominent simplifying assumptions that are often used to characterize bargaining solutions in theoretical models. Our study relies on a context-rich bargaining environment and varies the parameters of the bargaining problem along with the information that bargaining parties have about each other. Under the auxiliary assumption of selfishness, it aims at understanding whether bargaining is guided by abstract utilities as assumed by the classic version of cooperative bargaining theory or rather by comparisons in observables (e.g., money) as often assumed by behavioral models of decision-making. The experimental results show that welfarism and scale invariance are supported when the relevant information is only privately known. In general, bargaining outcomes are robust to rescaling that only affects the anchoring points of the utility scale (welfarism), but not to rescaling that affects the units on the utility scale (scale invariance). Overall, our experimental data deliver scarce empirical support to classic theoretical bargaining solutions based on abstract utility units. |
| Keywords: | Welfarism, Scale invariance, Individual rationality, Equal-division solution, Nash bargaining solution, Experiments, Bilateral bargaining |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05246963 |
| By: | Jonathan Teagan |
| Abstract: | This paper develops an economic model of the Open Source Intelligence (OSINT) attention economy in contemporary armed conflict. We conceptualize attention (e.g. social media views, followers, likes) as revenue, and time and risk spent in analysis as costs. Using utility functions and simple game theoretic setups, we show how OSINT actors (amateurs, journalists, analysts, and state operatives) allocate effort to maximize net attention benefit. We incorporate strategic behaviors such as a first mover advantage (racing to publish) and prisoner's dilemma scenarios (to share information or hold it back). In empirical case studies, especially the Ukraine conflict actors like the UAV unit Madyar's Birds and volunteer channels like Kavkazfighter, illustrate how battlefront reporting translates into digital revenue (attention) at real cost. We draw on recent literature and data (e.g., public follower counts, viral posts) to examine trends such as OSINT virality. Finally, we discuss policy implications for balancing transparency with operational security, citing calls for verification ethics and attention sustaining narratives. Our analysis bridges conflict studies and economics, highlighting OSINT as both a public good and a competitive product in today's information war. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.10548 |
| By: | Ren\'e A\"id; Philippe Bergault; Mathieu Rosenbaum |
| Abstract: | Recent regulation on intraday electricity markets has led to the development of shared order books with the intention to foster competition and increase market liquidity. In this paper, we address the question of the efficiency of such regulations by analysing the situation of two exchanges sharing a single limit order book, i.e. a quote by a market maker can be hit by a trade arriving on the other exchange. We develop a Principal-Agent model where each exchange acts as the Principal of her own market maker acting as her Agent. Exchanges and market makers have all CARA utility functions with potentially different risk-aversion parameters. In terms of mathematical result, we show existence and uniqueness of the resulting Nash equilibrium between exchanges, give the optimal incentive contracts and provide numerical solution to the PDE satisfied by the certainty equivalent of the exchanges. From an economic standpoint, our model demonstrates that incentive provision constitutes a public good. More precisely, it highlights the presence of a competitiveness spillover effect: when one exchange optimally incentivizes its market maker, the competing exchange also reaps indirect benefits. This interdependence gives rise to a free-rider problem. Given that providing incentives entails a cost, the strategic interaction between exchanges may lead to an equilibrium in which neither platform offers incentives -- ultimately resulting in diminished overall competition. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.10094 |