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on Game Theory |
| By: | Tushar Shankar Walunj; Shiksha Singhal; Veeraruna Kavitha; Jayakrishnan Nair |
| Abstract: | The Nash equilibrium (NE) is fundamental game-theoretic concept for characterizing stability in static strategic form games. However, at times, NE fails to capture outcomes in dynamic settings, where players' actions evolve over time in response to one another. In such cases, game dynamics fail to converge to an NE, instead exhibiting cyclic or oscillatory patterns. To address this, we introduce the concept of an 'equilibrium cycle' (EC). Unlike NE, which defines a fixed point of mutual best responses, an EC is a set-valued solution concept designed to capture the asymptotic or long-term behavior of dynamic interactions, even when a traditional best response does not exist. The EC identifies a minimal rectangular set of action profiles that collectively capture oscillatory game dynamics, effectively generalizing the notion of stability beyond static equilibria. An EC satisfies three important properties: \textit{stability} against external deviations (ensuring robustness), \textit{unrest} with respect to internal deviations (driving oscillation), and \textit{minimality} (defining the solution's tightness). This set-valued outcome generalizes the minimal curb set to discontinuous games, where best responses may not exist. In finite games, the EC also relates to sink strongly connected components (SCCs) of the best response graph. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.08471 |
| By: | Guillermo Alvarez; Ibrahim Ekren; Anastasis Kratsios; Xuwei Yang |
| Abstract: | Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately, only stylized Stackelberg games are explicitly solvable since the follower's best-response operator (as a function of the control of the leader) is typically analytically intractable. This paper addresses this issue by showing that the \textit{follower's best-response operator} can be approximately implemented by an \textit{attention-based neural operator}, uniformly on compact subsets of adapted open-loop controls for the leader. We further show that the value of the Stackelberg game where the follower uses the approximate best-response operator approximates the value of the original Stackelberg game. Our main result is obtained using our universal approximation theorem for attention-based neural operators between spaces of square-integrable adapted stochastic processes, as well as stability results for a general class of Stackelberg games. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09644 |
| By: | Wang Zhijian; Shan Lixia; Yao Qinmei; Wang Yijia |
| Abstract: | We conducted a laboratory experiment involving human subjects to test the theoretical hypothesis that equilibrium selection can be impacted by manipulating the games dynamics process, by using modern control theory. Our findings indicate that human behavior consists with the predictions derived from evolutionary game theory paradigm. The consistency is supported by three key observations: (1) the long-term distribution of strategies in the strategy space, (2) the cyclic patterns observed within this space, and (3) the speed of convergence to the selected equilibrium. These findings suggest that the design of controllers aimed at equilibrium selection can indeed achieve their theoretical intended purpose. The location of this study in the knowledge tree of evolutionary game science is presented. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.06847 |
| By: | Rosenmüller, Joachim (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | The Taxation Game is a cooperative game played between a set of countries $I$ = {$1, \ldots, n$} admitting the operation of a multinational enterprise (MNE, "the firm" ) within their jurisdiction. The firm, when operating within the territory of a subgroup $S {\subseteq} I$ of countries (a coalition) will generate a profit. Cooperating countries can agree about a share of the profit to be available for imposing taxes according to their rules and specifications, i.e., their tax rate or $tariff$. If the taxation basis, i.e., the profit obtained by the firm, is taken as the (monetary) value of the game, then we obtain a side payment or TU game, represented by a coalitional function $\stackrel{\circ}{\it{v}}$ defined on coalitions. This version is discussed by W. F. Richter. This author suggests that countries should agree on an allocation of the tax basis, i.e., the total profit $v(I)$ generated when the firm is operating in all participating countries. However, the profit obtained by the firm when (hypothetically) operating in in a subgroup (a coalition) $S {\subseteq} I$ of all countries should be taken into account. Consequently, the share of the tax basis alloted to a country should be determined by the Shapley value of the taxation game. The Shapley value "as a tool in theoretical economics" has widely been applied in Game Theory and Equilibrium Theory, but also in applications to Cost Sharing problems. We recall the Tenessee valley project, the determination of airport fees, and many others . By his approach Richter creates an interesting new field of applications. Within this paper we present a modification of this model by introducing the game $\stackrel{*}{\it{v}}$ dual to $\stackrel{\circ}{\it{v}}$. Moreover, we introduce the tariffs of countries, as the incentives of all parties involved (and actually of the firm) are based on their actual tax income depending on the tariffs. Then the resulting game is of NTU character and involves the tariffs. To this NTU game we apply a version of the Shapley NTU value. This way we characterize an agreement of the countries involved regarding the share of profit and the taxes resulting. A particular version of an NTU--game is given by a "bargaining problem" for $n$ countries. For simplicity of the argument we start out with this version and discuss the bargaining solution which are taylored versions of a Shapley version concept. We particularly deal with the Maschler-Perles solution based on superadditivity. Here, we focus on a suitable generalization of the Maschler-Perles solution. |
| Date: | 2024–11–11 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:695 |
| By: | Gagan Aggarwal; Anupam Gupta; Andres Perlroth; Grigoris Velegkas |
| Abstract: | We study a setting where agents use no-regret learning algorithms to participate in repeated auctions. \citet{kolumbus2022auctions} showed, rather surprisingly, that when bidders participate in second-price auctions using no-regret bidding algorithms, no matter how large the number of interactions $T$ is, the runner-up bidder may not converge to bidding truthfully. Our first result shows that this holds for \emph{general deterministic} truthful auctions. We also show that the ratio of the learning rates of the bidders can \emph{qualitatively} affect the convergence of the bidders. Next, we consider the problem of revenue maximization in this environment. In the setting with fully rational bidders, \citet{myerson1981optimal} showed that revenue can be maximized by using a second-price auction with reserves.We show that, in stark contrast, in our setting with learning bidders, \emph{randomized} auctions can have strictly better revenue guarantees than second-price auctions with reserves, when $T$ is large enough. Finally, we study revenue maximization in the non-asymptotic regime. We define a notion of {\em auctioneer regret} comparing the revenue generated to the revenue of a second price auction with truthful bids. When the auctioneer has to use the same auction throughout the interaction, we show an (almost) tight regret bound of $\smash{\widetilde \Theta(T^{3/4})}.$ If the auctioneer can change auctions during the interaction, but in a way that is oblivious to the bids, we show an (almost) tight bound of $\smash{\widetilde \Theta(\sqrt{T})}.$ |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09517 |
| By: | Jasmina Karabegovic |
| Abstract: | This paper introduces an explicit algorithm for computing perfect public equilibrium (PPE) payoffs in repeated games with imperfect public monitoring, public randomization, and discounting. The method adapts the established framework by Abreu, Pearce, and Stacchetti (1990) into a practical tool that balances theoretical accuracy with computational efficiency. The algorithm simplifies the complex task of identifying PPE payoff sets for any given discount factor {\delta}. A stand-alone implementation of the algorithm can be accessed at: https://github.com/jasmina-karabegovic/I RGames.git. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.01566 |
| By: | Awad, Emiel; Judd, Gleason; Riquelme, Nicolas |
| Abstract: | How do interest groups learn about and influence politicians over time? We develop a game-theoretic model where an interest group can lobby a politician while learning about their ideological alignment. Our analysis reveals a fundamental tradeoff: interest groups must balance gathering information against exerting immediate influence, while politicians strategically manage their reputations to shape future interactions. These strategic forces generate systematic dynamics: policies and transfers shift in tandem, with early-career politicians showing greater policy variance and extracting larger rents through reputation management than veterans. Uncertainty about alignment increases policy volatility as groups experiment with offers, while institutional features like committee power and revolving-door incentives systematically alter both learning incentives and influence strategies. Our results shed new light on how interest group influence evolves across political careers and varies with institutional context. |
| Date: | 2024–11–11 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:834vd |
| By: | Clayton, Christopher (Yale U); Maggiori, Matteo (Stanford U); Schreger, Jesse (Columbia U) |
| Abstract: | Governments use their countries’ economic strength from existing financial and trade relationships to achieve geopolitical and economic goals. We refer to this practice as geoeconomics. We build a framework based on three core ingredients: limited contract enforceability, input-output linkages, and externalities. Geoeconomic power arises from the ability to jointly exercise threats across separate economic activities. A hegemon, like the United States, exerts its power on firms and governments in its economic network by asking these entities to take costly actions that manipulate the world equilibrium in the hegemon’s favor. We characterize the optimal actions and show that they take the form of mark-ups on goods or higher rates on lending, but also import restrictions and tariffs. Input-output amplification makes controlling some sectors more valuable for the hegemon since changes in the allocation of these strategic sectors have a larger influence on the world economy. This formalizes the idea of economic coercion as a combination of strategic pressure and costly actions. We apply the framework to two leading examples: national security externalities and the Belt and Road Initiative. |
| JEL: | F02 P45 |
| Date: | 2024–01 |
| URL: | https://d.repec.org/n?u=RePEc:ecl:stabus:4174 |
| By: | Qiang Wan; Jun Cui |
| Abstract: | This paper explores the impact of banking fintech on reducing financial risks in the agricultural supply chain, focusing on the secondary allocation of commercial credit. The study constructs a three-player evolutionary game model involving banks, core enterprises, and SMEs to analyze how fintech innovations, such as big data credit assessment, blockchain, and AI-driven risk evaluation, influence financial risks and access to credit. The findings reveal that banking fintech reduces financing costs and mitigates financial risks by improving transaction reliability, enhancing risk identification, and minimizing information asymmetry. By optimizing cooperation between banks, core enterprises, and SMEs, fintech solutions enhance the stability of the agricultural supply chain, contributing to rural revitalization goals and sustainable agricultural development. The study provides new theoretical insights and practical recommendations for improving agricultural finance systems and reducing financial risks. Keywords: banking fintech, agricultural supply chain, financial risk, commercial credit, SMEs, evolutionary game model, big data, blockchain, AI-driven risk evaluation. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.07604 |
| By: | Matthew Gould (Department of Economics and Finance, Brunel University London, Cleveland Road, Uxbridge, UB8 2TL, UK); Matthew D. Rablen (School of Economics, University of Sheffield, Sheffield S1 4DT, UK) |
| Abstract: | We focus on the preferences of a salient group of highly-experienced individuals who are entrusted with making decisions that affect the lives of millions of their citizens, heads of government. We test for the presence of a fundamental behavioral bias, loss aversion, by examining heads of governments choice of decision rules for international organizations. Loss averse leaders would choose decision rules that oversupply negative (blocking) power at the expense of positive power (to initiate affirmative action), causing potential welfare losses through harmful policy persistence and reform deadlocks. If loss aversion is muted by experience and high-stakes it may not be exhibited in this context. We find evidence of significant loss aversion implied in the Qualified Majority rule of the Treaty of Lisbon, when understood as a Nash bargaining outcome. World leaders may be more loss averse than the populous they represent. |
| Keywords: | Loss aversion, Behavioral biases, Voting, Bargaining, Voting power, EU Council of Ministers |
| JEL: | D03 D81 D72 C78 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:shf:wpaper:2024011 |