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on Game Theory |
| By: | Endre Boros; Vladimir Gurvich; Kazuhisa Makino |
| Abstract: | We consider finite $n$-person deterministic graphical games and study the existence of pure stationary Nash-equilibrium in such games. We assume that all infinite plays are equivalent and form a unique outcome, while each terminal position is a separate outcome. It is known that for $n=2$ such a game always has a Nash equilibrium, while that may not be true for $n > 2$. A game is called {\em play-once} if each player controls a unique position and {\em terminal} if any terminal outcome is better than the infinite one for each player. We prove in this paper that play-once games have Nash equilibria. We also show that terminal games have Nash equilibria if they have at most three terminals. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.17387 |
| By: | Besner, Manfred |
| Abstract: | We present a new axiomatization of the proportional Shapley value. Our study is based on three axioms: efficiency, which ensures that the total worth of the grand coalition is fully distributed among the players; the disjointly productive players property, which states that removing a player who has no cooperative interactions with another player does not affect that player's payoff; and a new axiom that makes the difference to the classical Shapley value. This axiom, the coalitional substitution of players property, involves a scenario in which a player's cooperative contribution to one coalition is replaced by that of a group of new players whose combined individual worths match that of the original player. The key point is that the payoffs to the remaining players remain unaffected. |
| Keywords: | Cooperative game; Proportional Shapley value; Disjointly productive players; Coalitional substitution of players; Patronage refunds |
| JEL: | C71 D60 |
| Date: | 2025–02–19 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:124625 |
| By: | Gisèle Umbhauer |
| Abstract: | This paper completes two previous papers on the hammer-nail game. The hammer-nail game goes as follows: two players are in front of a nail slightly driven into a wooden support. Both have a hammer and in turn hit the nail. The winner is the first player able to fully drive the nail into the support. A player is of strength f if he is able, with one swing of the hammer, to drive the nail at most f millimeters into the support. A player is of non dexterity e if he is unable to hammer smoothly, so that, with one swing of the hammer, he drives the nail at least e millimeters into the support, with e >= 1. The two players may be of different strength and dexterity. In the two previous papers we studied this Nim-game by assuming that if the remaining distance is lower than e, then lack of dexterity is not a problem because one swing of the hammer necessarily drives the nail into the support. It followed that strength was more useful than dexterity to win the game. In this paper we suppose that a player destroys the support and loses the game if the remaining distance is lower than e. This new assumption completely changes the results: we now observe that dexterity becomes more useful than strength to win this new hammer-nail game. |
| Keywords: | Nim game, crossed cycles, Fort Boyard, subgame perfect Nash equilibrium, strength, dexterity. |
| JEL: | C72 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ulp:sbbeta:2024-39 |
| By: | \c{C}a\u{g}{\i}n Ararat; Zachary Feinstein |
| Abstract: | Systemic risk measures aggregate the risks from multiple financial institutions to find system-wide capital requirements. Though much attention has been given to assessing the level of systemic risk, less has been given to allocating that risk to the constituent institutions. Within this work, we propose a Nash allocation rule that is inspired by game theory. Intuitively, to construct these capital allocations, the banks compete in a game to reduce their own capital requirements while, simultaneously, maintaining system-level acceptability. We provide sufficient conditions for the existence and uniqueness of Nash allocation rules, and apply our results to the prominent structures used for systemic risk measures in the literature. We demonstrate the efficacy of Nash allocations with numerical case studies using the Eisenberg-Noe aggregation mechanism. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.20413 |
| By: | Elvio Accinelli (Facultad de Economia, Universidad Autonoma de San Luís Potosí, México); Atefeh Afsar (Mathematics Department, Allen University, Columbia, SC, United States); Filipe Martins (University of Coimbra, CeBER and Faculty of Economics); José Martins (LIAAD INESC TEC, Escola Superior de Tecnologia e Gestão, Politecnico de Leiria); Bruno Oliveira (LIAAD INESC TEC, Faculdade de Ciências da Nutrição e Alimentação, Universidade do Porto); Alberto A. Pinto (LIAAD–INESC TEC, Departmento de Matemática, Faculdade de Ciências, Universidade do Porto); Luis Quintas (Universidad de La Punta, San Luis, Argentina) |
| Abstract: | Baliga and Maskin introduced a model of contributions for the provisions of public goods such as contributing for the reduction of air pollution. In this work we consider an extended version of Baliga and Maskin's model with a parameter a which is the elasticity of the benefit function, and with heterogeneous agents, each with their own preferences for the good. For this generalized version of the model, we consider the formation of stable coalitions which are absorbing states of a bargaining Markov chain, where agents join or leave coalitions according to their cooperation and free-riding incentives. We show that there is a stable high coalition consisting of the set of agents most preferring/valuing the public good. The increase of the elasticity parameter a increases the size of the stable high coalition that changes from a single member (called the competitive coalition as appearing in Baliga and Maskin's paper) to the grand coalition involving all agents. However, the utility of members of the stable coalition can be very small when compared to the utility of the free-riders, rendering the formation of stable coalitions difficult. We show that a variant of the coalition folk theorem holds, meaning that member heterogeneity will tend to decrease the size of stable coalitions. We show that the formation of stable coalitions is subject to the paradox of cooperation, since even when stable coalitions are large and free-riders have not very low preferences for the public good, the utility of the stable coalition may still be low when compared to the full cooperation scenario of the grand coalition. However, the paradox does not hold when the free-riders have a very low preference for the public good, which also facilitates the spontaneous formation of stable coalitions, or when there are no free-riders and the grand coalition is stable, which is always the case when the elasticity a is large enough. |
| Keywords: | public and common goods, free-riding, coalitions, stability, Barrett's paradox of cooperation, Markov chains |
| JEL: | C7 D7 H4 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:gmf:papers:2025-03 |
| By: | Po-Hsuan Lin; Yen Ling Tan |
| Abstract: | We study how cursedness, the tendency to neglect how other people's strategies depend on their private information, affects information transmission in Spence's job market signaling game. We characterize the Cursed Sequential Equilibrium and show that as players become more cursed, the worker obtains less education -- a costly signal that does not enhance productivity -- suggesting that cursedness improves the efficiency of information transmission. However, this efficiency improvement depends on the richness of the message space. Revisiting the job market signaling experiment by K\"ubler, M\"uller, and Normann (2008), we find supportive evidence for our theory. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.19089 |
| By: | Joseph M. Ostroy; Joon Song |
| Abstract: | Connections are made between solution concepts for games in characteristic function form and Euler's Theorem underlying the neo-classical theory of distribution in which the total output produced is imputed to the marginal products of the inputs producing it. The assumptions for Euler's Theorem are constant returns (positive homogeneity) and differentiability of the production function. Representing characteristic functions in a vector space setting, marginal products of commodity inputs are translated as marginal products of individuals. Marginal products for discrete (resp. infinitesimal) individuals are defined by discrete (resp. infinitesimal) directional derivates. Additivity of directional derivatives underlies the definition of differentiability in both discrete and infinitesimal settings. A key distinction is between characteristic functions defined by von Neumann and Morgenstern (vNM) which do not necessarily exhibit concavity and characteristic function that do. A modification of the definition, interpreted as introducing ``property rights, '' implies concavity. The Shapley value is a redefinition of an individual's marginal product for a (vNM) characteristic function. Concave characteristic functions do not require such redefinition. Concave characteristic functions imply the existence of positively homogeneous saddle-function functions whose saddle-points represent equilbria of the game. The saddle-point property applies to games with populations consisting of any number of individuals each type. When there is a small integer number of each type, the saddle-point property is often, but not always, inconsistent with the Euler condition, that each individual receives its marginal contribution. Conversely, the saddle-point condition is typically, but not always, consistent with the Euler condition when there are a large number of each type. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.19424 |
| By: | LI, Hao; Wang, Gaowang |
| Abstract: | We develop a model economy with active financial markets, in which the policymaker's adoption of a gradualistic approach is a Bayesian Nash equilibrium. In addition to its financing role, the financial market also creates a channel for information revelation, encouraging the policymaker to take small policy steps. Smaller policy steps lead to more precise information about the productivity shock. Acquiring more information - both on the extensive margin and the intensive margin - provides sufficient incentives for the policymaker to consistently follow the gradualistic approach. This result holds robust for both exogenous and endogenous information models. |
| Keywords: | the gradualistic approach; active financial markets; information acquisition; endogenous information |
| JEL: | G1 O2 |
| Date: | 2025–04–18 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:124455 |
| By: | Nicole B\"auerle; Tamara G\"oll |
| Abstract: | In this paper, we consider $n$ agents who invest in a general financial market that is free of arbitrage and complete. The aim of each investor is to maximize her expected utility while ensuring, with a specified probability, that her terminal wealth exceeds a benchmark defined by her competitors' performance. This setup introduces an interdependence between agents, leading to a search for Nash equilibria. In the case of two agents and CRRA utility, we are able to derive all Nash equilibria in terms of terminal wealth. For $n>2$ agents and logarithmic utility we distinguish two cases. In the first case, the probabilities in the constraint are small and we can characterize all Nash equilibria. In the second case, the probabilities are larger and we look for Nash equilibria in a certain set. We also discuss the impact of the competition using some numerical examples. As a by-product, we solve some portfolio optimization problems with probability constraints. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.20340 |
| By: | Arve, Malin (Dept. of Business and Management Science, Norwegian School of Economics); Dyskeland, Ole Kristian (Dept. of Business and Management Science, Norwegian School of Economics); Foros, Øystein (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We analyze competition between two digital platforms selling subscriptions for unlimited access to their content catalogs (e.g., streaming and TV broadcasting platforms). A content provider offers additional content to the platforms. The content provider chooses between offering a revenue sharing contract and a per-consumer wholesale pricing contract towards the platforms, thereby endogenously determining whether its content will be distributed non-exclusively (on both platforms) or exclusively (on one platform). Our model yields clear predictions: In markets with low initial exclusivity, the content provider and both platforms prefer per-consumer wholesale pricing to endogenously promote non-exclusive distribution. Platforms set subscription prices that lead to full consumer singlehoming. Conversely, in markets with high initial exclusivity, all market players prefer a revenue-sharing contract that induces exclusive distribution, with platforms setting prices that encourage some consumers to multihome. |
| Keywords: | Multihoming; incremental pricing; content provision |
| JEL: | L13 L14 L82 |
| Date: | 2025–05–13 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhhfms:2025_017 |
| By: | Enrico De Monte; Bertrand Koebel |
| Abstract: | This paper characterizes the short- and long-run Cournot equilibrium with heterogeneous firms and stochastic technological change. In our model, firms have different technologies with heterogeneous fixed and variable costs and various degrees of markups. In a framework with homogeneous firms, Mankiw and Whinston (1986) show that the long-run Cournot equilibrium may be inefficient due to too many entries. We extend their result to the case of heterogeneous firms and show that higher industrial concentration of production is welfare improving. Using administrative data for French manufacturing firms, we estimate a wide degree of unobserved heterogeneity in both fixed and variable costs, and find a negative correlation between both. Our simulation results show that markups surprisingly only induce slight inefficiencies in the allocation of output, implying that it is almost compatible with welfare maximisation. Instead, firms’ choice to employ heterogeneous and often inefficient technologies turns out to harm more substantially welfare and aggregate output. |
| Keywords: | cost function, fixed cost, marginal cost, returns to scale, technological change, misallocation, markups, nonlinear least squares, panel data. |
| JEL: | L11 L60 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ulp:sbbeta:2025-01 |
| By: | Hua, Tony |
| Abstract: | People often avoid information to evade social obligations and justify selfish behavior. However, such behavior unfolds within a social context, where beliefs about others’ actions shape individual choices. This study examines how social expectations, shaped by perceived norms and decision framing, influence individuals’ willingness to avoid information. In a modified moral wiggle-room game, participants first predict how often others acquired information, then receive feedback about others’ information-seeking behavior before making their own decision as the dictator. The experiment manipulates (1) the feedback on norms participants receive, reflecting varying rates of information avoidance, and (2) whether they know in advance that they will be making the decision themselves, thereby inducing either a \textit{self-referential} or \textit{socially} framed perspective. Individuals were more likely to acquire information when exposed to norms favoring transparency, with pessimistic participants—those who believed ignorance was common—responding most strongly. Optimistic individuals showed little adjustment. Contrary to expectations, there was little evidence that participants distorted their beliefs about others to justify selfish behavior. However, a notable gender difference emerged: female participants, when primed with self-referential framing, were significantly less responsive to normative cues than males. Finally, an exploratory comparison with previous experiments suggests that belief elicitation itself, even in the absence of normative cues, significantly reduces information avoidance, highlighting a promising and scalable intervention for promoting transparency. |
| Keywords: | information avoidance; moral wiggle-room; social norms; social appropriateness; experiment |
| JEL: | C72 C91 D8 D83 |
| Date: | 2025–04–01 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:124363 |
| By: | Ziqi Li |
| Abstract: | This chapter discusses the opportunities of eXplainable Artificial Intelligence (XAI) within the realm of spatial analysis. A key objective in spatial analysis is to model spatial relationships and infer spatial processes to generate knowledge from spatial data, which has been largely based on spatial statistical methods. More recently, machine learning offers scalable and flexible approaches that complement traditional methods and has been increasingly applied in spatial data science. Despite its advantages, machine learning is often criticized for being a black box, which limits our understanding of model behavior and output. Recognizing this limitation, XAI has emerged as a pivotal field in AI that provides methods to explain the output of machine learning models to enhance transparency and understanding. These methods are crucial for model diagnosis, bias detection, and ensuring the reliability of results obtained from machine learning models. This chapter introduces key concepts and methods in XAI with a focus on Shapley value-based approaches, which is arguably the most popular XAI method, and their integration with spatial analysis. An empirical example of county-level voting behaviors in the 2020 Presidential election is presented to demonstrate the use of Shapley values and spatial analysis with a comparison to multi-scale geographically weighted regression. The chapter concludes with a discussion on the challenges and limitations of current XAI techniques and proposes new directions. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.00591 |