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on Game Theory |
| By: | Oliver Biggar; Iman Shames |
| Abstract: | The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation indicates the preferred choice for that player. We show that the preference graph is a surprisingly fundamental tool for studying normal-form games, which arises from natural axioms and which underlies many key game-theoretic concepts, including dominated strategies and strict Nash equilibria, as well as classes of games like potential games, supermodular games and weakly acyclic games. The preference graph is especially related to game dynamics, playing a significant role in the behaviour of fictitious play and the replicator dynamic. Overall, we aim to equip game theorists with the tools and understanding to apply the preference graph to new problems in game theory. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.03546 |
| By: | René Van den Brink (Department of Economics and Tinbergen Institute - VU University); Dinko Dimitrov (Saarland University); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne, CNRS - Université Paris 1 Panthéon-Sorbonne, Paris School of Economics) |
| Abstract: | Simple games in partition function form are used to model voting situations where a coalition being winning or losing might depend on the way players outside that coalition organize themselves. Such a game is called a plurality voting game if in every partition there is at least one winning coalition. In the present paper, we introduce a power index for this class of voting games and provide an axiomatic characterization. This power index is based on equal weight for every partition, equal weight for every winning coalition in a partition, and equal weight for each player in a winning coalition. Since some of the axioms we develop are conditioned on the power impact of losing coalitions becoming winning in a partition, our characterization heavily depends on a new result showing the existence of such elementary transitions between plurality voting games in terms of single embedded winning coalitions. The axioms restrict then the impact of such elementary transitions on the power of different types of players |
| Keywords: | axiomatization; power index; plurality game; winning coalition |
| JEL: | C71 D62 D72 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:mse:cesdoc:24014 |
| By: | Berliant, Marcus |
| Abstract: | We examine the fine microstructure of commuting in a game-theoretic setting with a continuum of commuters. Commuters' home and work locations can be heterogeneous. A commuter transport network is exogenous. Traffic speed is determined by local congestion at a time and place along a link, where local congestion at a time and place is endogenous. The model can be reinterpreted to apply to congestion on the internet. We find sufficient conditions for existence of equilibrium, that multiple equilibria are ubiquitous, and that the welfare properties of morning and evening commute equilibria differ on a generalization of a directed tree. |
| Keywords: | Commuting; Internet traffic; Congestion externality; Efficient Nash equilibrium; Price of anarchy |
| JEL: | L86 R41 |
| Date: | 2025–02–03 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:123553 |
| By: | Pongou, Roland; Sidie, Ghislain Junior |
| Abstract: | Ranked voting is an election format in which each voter ranks candidates on a ballot, and individual rankings are aggregated using a general rule to produce a social ranking. This paper proposes a non-cooperative model of this electoral system. The setting allows for unequal voting rights, abstention, and social incomparability of candidates, and each voter's utility is measured by how close his or her true preferences are to the social ranking. The analysis uncovers three main findings. First, it proves the existence of a pure strategy Nash equilibrium. Second, it shows that truthtelling is always a Nash equilibrium regardless of the voting rule and the structure of individual preferences. Third, under mild conditions, truthtelling is Pareto-efficient when voters have strict preferences. Extending the analysis to majoritarian elections with costly voluntary participation shows that truthtelling is an equilibrium if and only if the costs of participation are not too high and the election is tight. The findings have implications for the design of ranked voting systems that are compatible with truthtelling and efficiency while allowing unrestricted freedom in the choice of the voting rule. A reinterpretation of the model in the context of intrapersonal bargaining, where the decision-maker has multiple rational selves, has implications for the occurrence of cyclic individual choices that reflect stable and efficient behavioral patterns. |
| Date: | 2024–07–02 |
| URL: | https://d.repec.org/n?u=RePEc:wbk:wbrwps:10837 |
| By: | Antonio Cabrales; Gema Pomares; David Ramos Muñoz; Angel Sánchez |
| Abstract: | We study experimentally a new model to study the effect of climate externalities and contractual incompleteness on network formation. We model a network where good/green firms enjoy direct and indirect benefits from linking with one another. Bad/brown firms benefit from having a connection with a good firm, but they are a cost to both direct and indirect connections. In efficient networks the green firms should form large connected components with very few brown firms attached. The equilibrium networks, on the other hand, have many more brown firms attached, and components are also smaller than the efficient ones. Our experiments show that empirical results are broadly in line with the theoretical equilibrium predictions, although the precise quantitative outcomes are different from the theory. |
| Keywords: | network formation, climate change, contractual externalities, efficiency and equilibrium |
| JEL: | C92 D62 D85 Q54 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11663 |
| By: | Gregorio Curello; Sam Jindani |
| Abstract: | We propose a solution to the problem of bargaining with transfers, along with an axiomatisation of the solution. Inefficient allocations in the bargaining set can influence the solution, but are discounted relative to more efficient ones. The key axioms are additivity and a property we call \emph{inverse monotonicity}, which states that adding an allocation to the bargaining set that is worse for a given player than the initial solution cannot benefit that player. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.00308 |
| By: | Hanappi, Hardy |
| Abstract: | This paper combines one of the central questions of contemporary political economy, id est the conflict between China and the USA, with one of the major methodological advances in modelling technique, id est game theory. Of course, such a task goes far beyond the possibilities of a single research paper, it thus remains a modest sketch of a possible approach. No formalisation attempt is independent of the content it tries to model. Therefore, the first part of the paper provides a very short synopsis of the envisaged global conflict between the two superpowers. Surprisingly, one of the historical contributors to this topic, John von Neumann, also is the scientist, which brought the methodological revolution of game theory to its full blossoming. The second part of the paper discusses von Neumann’s vision of game theory as a new formal language to describe human interaction - a somewhat different vision to the one that drove the mathematicians using his approach in the decades that followed. The third part of the paper presents a simple simulation exercise built on the ideas of the first two parts. The conclusion provides two lessons that can be learned from the paper, a methodological one and one concerning the mid-run development of the conflict between China and the USA. |
| Keywords: | Geopolitical dynamics; Applied Game Theory; Cold War |
| JEL: | F01 F50 F54 F55 P16 |
| Date: | 2025–01–31 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:123517 |
| By: | Stefan P. Penczynski (School of Economics and Centre for Behavioural and Experimental Social Science, University of East Anglia); Christian Koch (Department of Economics, University of Vienna); Sihong Zhang (McKinsey & Company, Inc.) |
| Abstract: | This study investigates experimentally information disclosure in settings with and without seller competition. Sellers often choose to report information selec-tively and buyers account for this—even though not fully—by bidding skeptically. As expected, competition increases sellers’ information disclosure but leads, sur-prisingly and replicably, to more buyer na¨ıvety, offsetting the welfare benefits from improved disclosure. A framing effect generates this result: merely describing a situation as competitive rather than monopolistic alters buyer behavior. Akin to the so-called Peltzman effect, buyers seemingly perceive competition as a safer en-vironment to which they behaviorally adapt by abandoning their skepticism. Con-sequently, consumer benefits hinge on perceived competitiveness—a vulnerability firms may leverage to their advantage. |
| Keywords: | Disclosure, verifiable information, competition, Peltzman effect |
| JEL: | D40 D83 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:uea:wcbess:25-01 |
| By: | Cañón Salazar, Carlos (Bank of England); Tanaka, Misa (Bank of England); Thanassoulis, John (Warwick Business School, University of Warwick and CEPR and UK Competition and Markets Authority) |
| Abstract: | We develop a game-theoretic model in which financial regulators compete to attract internationally mobile banks by setting the level of regulatory stringency to meet both financial stability and growth objectives. We show that competitive deregulation will not arise if the relatively growth-focused regulator becomes even more growth focused, but it becomes more likely if the relatively stability-focused regulator becomes more growth focused. We also demonstrate that domestic nonregulatory inducements to retain banks (eg tax, labour laws) create an externality on the global equilibrium of regulatory stringency chosen by financial regulators with a growth objective. |
| Keywords: | Financial regulation; global financial markets; growth; competitiveness |
| JEL: | F43 G18 G28 L50 |
| Date: | 2024–12–06 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:1098 |