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on Game Theory |
| By: | Lu Yu |
| Abstract: | Two theorems announced by Topkis about the topological description of sublattices are proved. They are applied to extend some classical results concerning the existence and the order structure of Nash equilibria of certain supermodular games, with some problems in Zhou's proof corrected. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.09582&r= |
| By: | René Van Den Brink (Department of Economics and Tinbergen Institute, VU University, Amsterdam, The Netherlands); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne, CNRS, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics) |
| Abstract: | This paper aims to connect the social network literature on centrality measures with the economic literature on von Neumann-Morgenstern expected utility functions using cooperative game theory. The social network literature studies various concepts of network centrality, such as degree, betweenness, connectedness, and so on. This resulted in a great number of network centrality measures, each measuring centrality in a different way. In this paper, we aim to explore which centrality measures can be supported as von Neumann-Morgenstern expected utility functions, reflecting preferences over different network positions in different networks. Besides standard axioms on lotteries and preference relations, we consider neutrality to ordinary risk. We show that this leads to a class of centrality measures that is fully determined by the degrees (i.e. the numbers of neighbours) of the positions in a network. Although this allows for externalities, in the sense that the preferences of a position might depend on the way how other positions are connected, these externalities can be taken into account only by considering the degrees of the network positions. Besides bilateral networks, we extend our result to general cooperative TU-games to give a utility foundation of a class of TU-game solutions containing the Shapley value |
| Keywords: | group decisions and negotiations; weighted graph; degree centrality; von Neumann-Morgenstern expected utility function; cooperative game |
| JEL: | D85 D81 C02 |
| Date: | 2023–08 |
| URL: | https://d.repec.org/n?u=RePEc:mse:cesdoc:23012r&r= |
| By: | Danyang Jia (School of Cybersecurity, Northwestern Polytechnical University and School of Artificial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, CHINA); Ivan Romic (School of Artificial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, CHINA, Center for Computational Social Science, Kobe University, and Research Institute for Economics and Business Administration, Kobe University, JAPAN); Lei Shi (School of Statistics and Mathematics, Yunnan University of Finance and Economics, CHINA); Qi Su (Department of Automation, Shanghai Jiao Tong University, Key Laboratory of System Control and Information Processing, Ministry of Education of China, and Shanghai Engineering Research Center of Intelligent Control and Management, CHINA); Chen Liu (School of Ecology and Environmental Sciences, Northwestern Polytechnical University, CHINA); Jinzhuo Liu (School of Software, Yunnan University, CHINA); Petter Holme (Center for Computational Social Science, Kobe University, JANPAN and Department of Computer Science, Aalto University, FINLAND); Xuelong Li (School of Cybersecurity, Northwestern Polytechnical University and School of Artificial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, CHINA); Zhen Wang (School of Cybersecurity, Northwestern Polytechnical University and School of Artificial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, CHINA) |
| Abstract: | The awareness of individuals regarding their social network surroundings and their capacity to use social connections to their advantage are well-established human characteristics. Economic games, incorporated with network science, are frequently used to examine social behaviour. Traditionally, such game models and experiments artificially limit players' abilities to take varied actions toward distinct social neighbours (i.e., to operate their social networks). We designed an experimental paradigm that alters the degree of social network agency to interact with individual neighbours, and applied it to the prisoner's dilemma (N = 735), trust game (N = 735), and ultimatum game (N = 735) to investigate cooperation, trust, and fairness. The freedom to interact led to more prosocial behaviour across all three economic games and resulted in higher wealth and lower inequality compared to controls without such freedom. These findings suggest that human behaviour is more prosocial than current science indicates. |
| Keywords: | Behavioural science; Networks; Cooperation; Prosociality |
| Date: | 2023–03 |
| URL: | https://d.repec.org/n?u=RePEc:kob:dpaper:dp2023-11&r= |
| By: | Matthew I. Jones |
| Abstract: | We introduce a new framework to study the group dynamics and game-theoretic considerations when voters in a committee are allowed to trade votes. This model represents a significant step forward by considering vote-for-vote trades in a low-information environment where voters do not know the preferences of their trading partners. All voters draw their preference intensities on two issues from a common probability distribution and then consider offering to trade with an anonymous partner. The result is a strategic game between two voters that can be studied analytically. We compute the Nash equilibria for this game and derive several interesting results involving symmetry, group heterogeneity, and more. This framework allows us to determine that trades are typically detrimental to the welfare of the group as a whole, but there are exceptions. We also expand our model to allow all voters to trade votes and derive approximate results for this more general scenario. Finally, we emulate vote trading in real groups by forming simulated committees using real voter preference intensity data and computing the resulting equilibria and associated welfare gains or losses. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.09536&r= |
| By: | Matthes, Julian; Piazolo, David |
| Abstract: | Road cycling races, although won by individual riders, are a competition of teams. Riding behind other riders significantly reduces the energy required to hold a given speed. These races thus provide free-riding incentives. We introduce a game-theoretic framework of this strategic setup to analyze a team’s winning probability in various race situations and to examine group characteristics facilitating coordination. We complement our theoretical results with an empirical analysis using data from more than 40 seasons of professional road cycling races. Our model suggests that asymmetry in rider strength or team strength within a group is favorable for group coordination. Also, adding teammates to competing groups is beneficial because it leads to strategic benefits, increasing the free-riding opportunities in both groups. We find empirical evidence that a teammate in a group behind has a positive impact on win probability, indicating that such an effect indeed exists. |
| Keywords: | Coopetition; Free-riding; Diversification; Coordination; Sports Economics |
| Date: | 2024–06–24 |
| URL: | https://d.repec.org/n?u=RePEc:awi:wpaper:0751&r= |
| By: | Miettinen, Topi; Vanberg, Christoph |
| Abstract: | We theoretically investigate how the application of unanimity rule can lead to inefficient delay in collective decision making. We do so in the context of a distributive multilateral bargaining model featuring strategic pre-commitment. Prior to each bargaining round, players can declare a minimum share that they must receive in return for their vote. Such declarations become binding with an exogenously given probability. We characterize the set of stationary subgame perfect equilibria under all q-majority rules. Our results suggest that unanimity rule is uniquely inefficient. All other rules, including all-but-one, are fully efficient. |
| Keywords: | bargaining; commitment; conflict; delay; international negotiations; climate negotiations; legislative; multilateral; voting; majority; unanimity |
| Date: | 2024–06–25 |
| URL: | https://d.repec.org/n?u=RePEc:awi:wpaper:0749&r= |
| By: | Moshe Babaioff; Linda Cai; Brendan Lucier |
| Abstract: | We consider a principal seller with $m$ heterogeneous products to sell to an additive buyer over independent items. The principal can offer an arbitrary menu of product bundles, but faces competition from smaller and more agile single-item sellers. The single-item sellers choose their prices after the principal commits to a menu, potentially under-cutting the principal's offerings. We explore to what extent the principal can leverage the ability to bundle product together to extract revenue. Any choice of menu by the principal induces an oligopoly pricing game between the single-item sellers, which may have multiple equilibria. When there is only a single item this model reduces to Bertrand competition, for which the principal's revenue is $0$ at any equilibrium, so we assume that no single item's value is too dominant. We establish an upper bound on the principal's optimal revenue at every equilibrium: the expected welfare after truncating each item's value to its revenue-maximizing price. Under a technical condition on the value distributions -- that the monopolist's revenue is sufficiently sensitive to price -- we show that the principal seller can simply price the grand-bundle and ensure (in any equilibrium) a constant approximation to this bound (and hence to the optimal revenue). We also show that for some value distributions violating our conditions, grand-bundle pricing does not yield a constant approximation to the optimal revenue in any equilibrium. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.13835&r= |
| By: | Sylvain Béal (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France); David Lowing (Laboratoire de Génie Industriel, CentraleSupélec, Université Paris-Saclay, France); Léa Munich (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France and Université de Lorraine, BETA, F-54000 Nancy, France) |
| Abstract: | We consider the problem of sharing the cost of cleaning the non-point source pollution of industrial sites among the firms that own these sites. The bilateral liabilities between firms are depicted by an undirected graph. We introduce and characterize axiomatically two allocation rules inspired by the celebrated Polluter pays and Beneficiary pays principles in environmental law. The first one shares evenly the cost of cleaning up a site among the firms that can have caused the corresponding environmental damage. The second one charges to each firm the entire cost of cleaning up its own production site. We also establish connections with cooperative game theory. |
| Keywords: | Cooperative game theory; Cost allocation; Pollution; liability |
| JEL: | C71 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:crb:wpaper:2024-13&r= |
| By: | Giovanni Valvassori Bolg\`e |
| Abstract: | A set of agents has to make a decision about the provision of a public good and its financing. Agents have heterogeneous values for the public good and each agent's value is private information. An agenda-setter has the right to make a proposal about a public-good level and a vector of contributions. For the proposal to be approved, only the favourable votes of a subset of agents are needed. If the proposal is not approved, a type-dependent outside option is implemented. I characterize the optimal public-good provision and the coalition-formation for any outside option in dominant strategies. Optimal public-good provision might be a non-monotonic function of the outside option public-good level. Moreover, the optimal coalition might be a non-convex set of types. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.08936&r= |
| By: | Jose M. Betancourt (Yale University); Ali Horta su (University of Chicago); Aniko …ry (Carnegie Mellon University); Kevin R. Williams (Yale University) |
| Abstract: | We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with the lowest remaining capacity sells. Because firms do not fully internalize the social option value of future sales, equilibrium prices can be inefficiently low such that both firms and consumers would benefit if firms could commit to higher prices. We term this new welfare effect the Bertrand scarcity trap. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2394&r= |
| By: | Johannes Schneider; \'Alvaro Delgado-Vega |
| Abstract: | We study an organization with a principal and two agents. All three have a long-run agenda which drives their repeated interactions. The principal can influence the competition for agency by endorsing an agent. Her agenda is more aligned with her ``friend'' than with her ``enemy.'' Even when fully aligned with the friend, the principal embraces the enemy by persistently endorsing him once an initial ``cordon sanitaire'' to exclude the enemy breaks exogenously. A dynamically optimizing principal with extreme agenda either implements the commitment solution or reverts to static Nash. For less extreme principals, losing commitment power has more gradual effects. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.09734&r= |
| By: | Ivan Guo; Shijia Jin; Kihun Nam |
| Abstract: | In continuation of the macroscopic market making \`a la Avellaneda-Stoikov as a control problem, this paper explores its stochastic game. Concerning the price competition, each agent is compared with the best quote from the others. We start with the linear case. While constructing the solution directly, the ordering property and the dimension reduction in the equilibrium are revealed. For the non-linear case, extending the decoupling approach, we introduce a multidimensional characteristic equation to study the well-posedness of forward-backward stochastic differential equations. Properties of coefficients in the characteristic equation are obtained via non-smooth analysis. In addition to novel well-posedness results, the linear price impact arises and the impact function can be further decomposed into two parts in some examples. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.05662&r= |
| By: | Mauricio Bugarin; Wilfredo Leiva Maldonado |
| Abstract: | This paper proposes an innovative methodology for sequential auctions of homogeneous goods that creates asymmetry among participants, thereby achieving higher revenue for the auctioneer. The asymmetry arises endogenously from a competitive advantage in the second auction granted to the winner of the first auction. The analysis shows that the auctioneer's expected revenue in this scenario is higher than in auctions without a competitive advantage and approaches the expected revenue of an optimal reserve price auction. After analyzing the benefits and drawbacks of the competitive advantage mechanism, this paper concludes that it represents a more effective auction design than conventional approaches. |
| Keywords: | Sequential auctions; Endogenous asymmetry; Strategic advantage |
| JEL: | D44 D47 |
| Date: | 2024–07–01 |
| URL: | https://d.repec.org/n?u=RePEc:spa:wpaper:2024wpecon21&r= |
| By: | José Pedro Pontes; João Dias |
| Abstract: | This paper examines the recent evolution of higher education in Portugal under the light of an n-person coordination game. We feature two alternative coordination requirements, namely “unanimity”, which expresses a cooperative agreement, and “k-coordination”, which is driven by efficiency considerations. We find that public policy has driven higher education to fully cover the territory and in particular individuals living in sparsely populated areas. This orientation might have brought about a loss of scale economies in teaching and, consequently, in the efficiency of tertiary education. This is a plausible explanation for the disconnection between higher education spread and economic growth during the more recent period. |
| Keywords: | Education, Regional Development, Coordination Games, Risk Dominance. |
| JEL: | C72 I20 O12 R11 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:ise:remwps:wp03302024&r= |