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on Game Theory |
| By: | Yiyin Cao; Chuangyin Dang |
| Abstract: | The concept of Nash equilibrium in behavioral strategies (NashEBS) was formulated By Nash~\cite{Nash (1951)} for an extensive-form game through global rationality of nonconvex payoff functions. Kuhn's payoff equivalence theorem resolves the nonconvexity issue, but it overlooks that one Nash equilibrium of the associated normal-form game can correspond to infinitely many NashEBSs of an extensive-form game. To remedy this multiplicity, the traditional approach as documented in Myerson~\cite{Myerson (1991)} involves a two-step process: identifying a Nash equilibrium of the agent normal-form representation, followed by verifying whether the corresponding mixed strategy profile is a Nash equilibrium of the associated normal-form game, which often scales exponentially with the size of the extensive-form game tree. In response to these challenges, this paper develops a characterization of NashEBS through the incorporation of an extra behavioral strategy profile and beliefs, which meet local sequential rationality of linear payoff functions and self-independent consistency. This characterization allows one to analytically determine all NashEBSs for small extensive-form games. Building upon this characterization, we acquire a polynomial system serving as a necessary and sufficient condition for determining whether a behavioral strategy profile is a NashEBS. An application of the characterization yields differentiable path-following methods for computing such an equilibrium. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.00529 |
| By: | Motoki Otsuka |
| Abstract: | Graphon games are a class of games with a continuum of agents, introduced to approximate the strategic interactions in large network games. The first result of this study is an equilibrium existence theorem in graphon games, under the same conditions as those in network games. We prove the existence of an equilibrium in a graphon game with an infinite-dimensional strategy space, under the continuity and quasi-concavity of the utility functions. The second result characterizes Nash equilibria in graphon games as the limit points of asymptotic Nash equilibria in large network games. If a sequence of large network games converges to a graphon game, any convergent sequence of asymptotic Nash equilibria in these large network games also converges to a Nash equilibrium of the graphon game. In addition, for any graphon game and its equilibrium, there exists a sequence of large network games that converges to the graphon game and has asymptotic Nash equilibria converging to the equilibrium. These results suggest that the concept of a graphon game is an idealized limit of large network games as the number of players tends to infinity. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.01944 |
| By: | Rosenmüller, Joachim (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We continue the discussion of the taxation game following our presentation in [12]. Our concept describes a cooperative game played between a set of jurisdictions (“ countries”). These players admit the operation of a multinational enterprise (MNE, the “firm”) within their jurisdiction. The original version of this game is due to W. F. Richter [3], [4]. We suggest an extension of the model by introducing the dual game of the firm’s profits and the tax function game. The latter is the NTU game generated by introducing tax functions (the term “tariffs” will be avoided henceforth). In [12] we treated the bargaining situation obtained when all countries decide to cooperate – otherwise everyone will fall back on their status quo point. However, in his basic paper, Richter argues that the share of the tax basis allotted to a country should be determined by the Shapley value of the taxation game. This idea establishes an interesting new field of applications. The Shapley value “as a tool in theoretical economics” [13], [14] has widely been applied in Game Theory, Equilibrium Theory, applications to Cost Sharing problems, Airport Landing Fee games, and many others. Based on these ideas, we continue our presentation by formulating the tax function game for the countries involved and introducing the Maschler–Perles–Shapley value as developed in [11]. To this end, we introduce the adjusted TU game, which reflects a rescaling of utility measurement as suggested by the superadditivity axiom of the Maschler–Perles solution. Then the Maschler–Perles–Shapley value of the tax function game is the image of the Shapley value of the adjusted TU game on the Pareto surface of the grand coalition. We demonstrate that the Maschler-Perles–Shapley value for the tax function game is Pareto efficient, covariant with affine transformations of utility, and anonymous. |
| Date: | 2025–04–23 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:704 |
| By: | Arunava Patra; Joy Das Bairagya; Sagar Chakraborty |
| Abstract: | The symbiotic relationship between the frameworks of classical game theory and evolutionary game theory is well-established. However, evolutionary game theorists have mostly tapped into the classical game of complete information where players are completely informed of all other players' payoffs. Of late, there is a surge of interest in eco-evolutionary interactions where the environment's state is changed by the players' actions which, in turn, are influenced by the changing environment. However, in real life, the information about the true environmental state must pass through some noisy channel (like usually imperfect sensory apparatus of the players) before it is perceived by the players: The players naturally are prone to sometimes perceive the true state erroneously. Given the uncertain perceived environment, the players may adopt bet-hedging kind of strategies in which they play different actions in different perceptions. In a population of such ill-informed players, a player would be confused about the information state of her opponent, and an incomplete information situation akin to a Bayesian game surfaces. In short, we contemplate possibility of natural emergence of symbiotic relationship between the frameworks of Bayesian games and eco-evolutionary games when the players are equipped with inefficient sensory apparatus. Herein, we illustrate this connection using a setup of infinitely large, well-mixed population of players equipped with two actions for exploiting a resource (the environment) at two different rates so that the resource state evolves accordingly. The state of the resource impacts every player's decision of playing particular action. We investigate continuous state environment in the presence of a Gaussian noisy channel. Employing the formalism of replicator dynamics, we find that noisy information can be effective in preventing resource from going extinct. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.02399 |
| By: | Olivier Bos; Martin Pollrich |
| Abstract: | We study optimal auctions in a symmetric private values setting, where bidders have signaling concerns: they care about winning the object and a receivers inference about their type. Signaling concerns arise in various economic situations such as takeover bidding, charity auctions, procurement and art auctions. We show that auction revenue can be decomposed into the standard revenue from the respective auction without signaling concern, and a signaling component. The latter is the bidders' ex-ante expected signaling value net of an endogenous outside option: the signaling value for the lowest type. The revenue decomposition restores revenue equivalence between different auction designs, provided that the same information about bids is revealed. Revealing information about submitted bids affects revenue via the endogenous outside option. In general, revenue is not monotone in information revelation: revealing more information about submitted bids may reduce revenue. We show that any bid disclosure rule allowing to distinguish whether a bidder submitted a bid or abstained from participation minimizes the outside option, and therefore maximizes revenue. |
| Keywords: | optimal auctions, revenue equivalence, Bayesian persuasion, information design |
| JEL: | D44 D82 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11723 |
| By: | Alif Aqsha; Philippe Bergault; Leandro S\'anchez-Betancourt |
| Abstract: | We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader-follower stochastic game, where the venue is the leader and a representative LP is the follower. We derive approximate closed-form equilibrium solutions to the stochastic game and analyze the reward structure. Our findings suggest that under the equilibrium contract, LPs have incentives to add liquidity to the pool only when higher liquidity on average attracts more noise trading. The equilibrium contract depends on the external price, the pool reference price, and the pool reserves. Our framework offers insights into AMM design for maximizing order flow while ensuring LP profitability. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.22502 |
| By: | Pierre Bousseyroux; Gilles Z\'erah; Michael Benzaquen |
| Abstract: | Stabilizing cooperation among self-interested individuals presents a fundamental challenge in evolutionary theory and social science. While classical models predict the dominance of defection in social dilemmas, empirical and theoretical studies have identified various mechanisms that promote cooperation, including kin selection, reciprocity, and spatial structure. In this work, we investigate the role of localized imitation in the evolutionary dynamics of cooperation within an optional Public Goods Game (PGG). We introduce a model where individuals belong to distinct groups and adapt their strategies based solely on comparisons within their own group. We identify different dynamical regimes, including stable fixed points, limit cycles, and Rock-Scissors-Paper-type oscillations. Our analysis, grounded in a replicator-type framework, reveals that such group-level imitation can stabilize cooperative behavior, provided that groups are not initially polarized around a single strategy. In other words, restricting imitation to group-level interactions mitigates the destabilizing effects of global competition, providing a potential explanation for the resilience of cooperation in structured populations. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.05086 |
| By: | Ran Eilat; Zvika Neeman; Eilon Solan |
| Abstract: | In this note, we propose an alternative definition of strategies and histories in opportunity hunting games, as introduced in Eilat, Neeman and Solan (2025). The advantage of the formulation presented here is that it encompasses a broader class of strategies than the inertial strategies analyzed in Eilat, Neeman and Solan (2025), including those that allow for a countably infinite number of inspections within finite time intervals. Although the definitions of histories and strategies in this broader setting are more subtle, we show that the main results continue to hold. This demonstrates that the findings in Eilat, Neeman and Solan (2025) are robust to environments in which players have access to a richer strategy space. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.23437 |
| By: | Ciamac C. Moallemi; Mallesh M. Pai; Dan Robinson |
| Abstract: | In financial applications, latency advantages - the ability to make decisions later than others, even without the ability to see what others have done - can provide individual participants with an edge by allowing them to gather additional relevant information. For example, a trader who is able to act even milliseconds after another trader may receive information about changing prices on other exchanges that lets them make a profit at the expense of the latter. To better understand the economics of latency advantages, we consider a common-value auction with a reserve price in which some bidders may have more information about the value of the item than others, e.g., by bidding later. We provide a characterization of the equilibrium strategies and study the welfare and auctioneer revenue implications of the last-mover advantage. We show that the auction does not degenerate completely and that the seller is still able to capture some value. We study comparative statics of the equilibrium under different assumptions about the nature of the latency advantage. Under the assumptions of the Black-Scholes model, we derive formulas for the last mover's expected profit, as well as for the sensitivity of that profit to their timing advantage. We apply our results to the design of blockchain protocols that aim to run auctions for financial assets on-chain, where incentives to increase timing advantages can put pressure on the decentralization of the system. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.02077 |
| By: | Alfred A. B. Mayaki |
| Abstract: | Prior literature on two-firm two-market and two-stage extended dynamic models has introduced what Guth (2016) succinctly terms a social dilemma. A state in which conglomerate firms competing in a Bertrand duopoly consider jointly optimizing profits under a tacit self-enforcing agreement to deter market entry. This theoretical article reinterprets the social dilemma highlighted by Guth (2016) not only in the context of allocation but also through the lens of competition where entry must legally be permitted even if cooperative signalling would otherwise sustain joint profitability. This study explores the significance of a sufficiency condition on each firms non-instantaneous reaction function requiring the maintenance of a stable long-run equilibrium through retaliative restraint characterized by either two negative eigenvalues or a saddle-path trajectory. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.22825 |
| By: | Jiang, Shuguang (Shandong University); Villeval, Marie Claire (CNRS); Zhang, Zhengping (Shandong University); Zheng, Jie (Shandong University) |
| Abstract: | We experimentally study how economic prospects and power shifts affect the risk of conflict through a dynamic power rivalry game. Players decide whether to maintain the status quo or challenge a rival under declining, constant, or growing economic prospects. We find that conflict rates are highest when economic prospects decline and lowest when they improve. A behavioral model incorporating psychological costs and reciprocity can explain these differences. A survey on U.S.-China relations supports the real-world relevance of these findings. Inspired by the Thucydides’s Trap, this study highlights how economic expectations shape conflict dynamics, offering key insights into geopolitical stability. |
| Keywords: | conflict, economic prospects, Thucydides’s Trap, power shift, experiment |
| JEL: | C83 C91 D74 D91 F51 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17823 |
| By: | John S. McAlister; Jesse L. Brunner; Danielle J. Galvin; Nina H. Fefferman |
| Abstract: | Global trade of material goods involves the potential to create pathways for the spread of infectious pathogens. One trade sector in which this synergy is clearly critical is that of wildlife trade networks. This highly complex system involves important and understudied bidirectional coupling between the economic decision making of the stakeholders and the contagion dynamics on the emergent trade network. While each of these components are independently well studied, there is a meaningful gap in understanding the feedback dynamics that can arise between them. In the present study, we describe a general game theoretic model for trade networks of goods susceptible to contagion. The primary result relies on the acyclic nature of the trade network and shows that, through the course of trading with stochastic infections, the probability of infection converges to a directly computable fixed point. This allows us to compute best responses and thus identify equilibria in the game. We present ways to use this model to describe and evaluate trade networks in terms of global and individual risk of infection under a wide variety of structural or individual modifications to the trade network. In capturing the bidirectional coupling of the system, we provide critical insight into the global and individual drivers and consequences for risks of infection inherent in and arising from the global wildlife trade, and any economic trade network with associated contagion risks. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.06905 |
| By: | Michelle R. Garfinkel; Constantinos Syropoulos |
| Abstract: | We consider a dynamic setting where two countries with competing claims to a resource/asset first arm and then choose whether to resolve their dispute through war or peacefully through settlement. War precludes international trade and can be destructive, but also locks gains and eliminates arming costs in the future. By contrast, a peaceful resolution, possibly supported by arming, avoids destruction and allows for mutually advantageous trade; yet future settlements must be renegotiated under the threat of war. We characterize the conditions under which peace is stable and show that, depending on war’s destructiveness, time preferences, and the distribution of resource endowments, greater gains from trade can pacify international tensions, but possibly only for more uneven endowment distributions. |
| Keywords: | interstate war, armed peace, unarmed peace, security policies, gains from trade, shadow of the future. |
| JEL: | C72 C78 D30 D70 D74 F10 F51 F60 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11802 |
| By: | Yike Wang |
| Abstract: | In this paper, we extend the research on time-consistent stochastic control problems with higher-order moments, as formulated by [Y. Wang et al. SIAM J. Control. Optim., 63 (2025), in press]. We consider a linear controlled dynamic equation with state-dependent diffusion, and let the sum of a conventional mean-variance utility and a fairly general function of higher-order central moments be the objective functional. We obtain both the sufficiency and necessity of the equilibrium condition for an open-loop Nash equilibrium control (ONEC), under some continuity and integrability assumptions that are more relaxed and natural than those employed before. Notably, we derive an extended version of the stochastic Lebesgue differentiation theorem for necessity, because the equilibrium condition is represented by some diagonal processes generated by a flow of backward stochastic differential equations whose the data do not necessarily satisfy the usual square-integrability. Based on the derived equilibrium condition, we obtain the algebra equation for a deterministic ONEC. In particular, we find that the mean-variance equilibrium strategy is an ONEC for our higher-order moment problem if and only if the objective functional satisfies a homogeneity condition. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.04113 |
| By: | Peter Achim; Jan Knoepfle |
| Abstract: | A principal continually decides whether to approve resource allocations to an agent, who exerts private effort to remain eligible. The principal must perform costly inspections to determine the agent's eligibility. We characterize Markov Perfect Equilibria and analyze the paths of trust and oversight that emerge from the dynamic interplay of effort and oversight. At high trust levels, effort is an intertemporal substitute to oversight, which leads to unique interior effort choices and random inspections. At low trust levels, effort is an intertemporal complement to oversight, which may create a coordination problem, leading to equilibrium multiplicity. Voluntary disclosure can mitigate this coordination issue. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.02696 |
| By: | Nirjhor, Sams Afif; Liu, Fangyue; Nakamaru, Mayuko |
| Abstract: | A general supply chain is a division of labor of an arbitrary number of subtasks, which has asymmetric interactions among the subtask-holder groups. To sustain a supply chain, cooperation among the subtask-holders is a must. We construct a general network model of supply chain with a finite number of roles with a single output, where the supply of faulty products is possible and a supply chain never stops on the way. We consider that cooperators and defectors exist in each subtask-holder group in a supply chain; cooperators of a subtask-holder group pay a cost of cooperation to maintain and upgrade the quality of the product, defectors however do not pay any cost, and thus the product quality reduces. In some supply chains, more cooperators upgrade the quality of the product more, and players can obtain a better reputation defined as a bonus that is given to all players. We found that the supply chain with a bonus confronts the social dilemma. We make replicator equations of asymmetric games to investigate the evolution of cooperation in a supply chain. We found that not the benefit from supply but the cost of cooperation influences the dynamics. As a result, the network structure of the supply chain never influences the dynamics. Sanction on the defectors induces the evolution of cooperation and non-linear bonus functions promote co-existences of cooperator groups and defector groups. The bonus functions determine whether the length of the supply chain promotes the evolution of cooperation or not. |
| Date: | 2025–04–24 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:3679n_v1 |
| By: | Daniel Heyen; Alessandro Tavoni |
| Abstract: | GoBs are goods for which agents have non-monotonic preferences: more is beneficial only up to an ideal level, beyond which additional quantities become undesirable. We analyze public GoBs (non-excludable and non-rival) through a theoretical framework applicable to diverse contexts such as solar geoengineering, wildlife management, and defense spending of European countries. The private provision of public GoBs proves inefficient due to both free-rider and free-driver externalities. Contribution costs and heterogeneity in ideal levels determine equilibrium outcomes. Surprisingly, reducing contribution costs can decrease welfare when agents' preferences diverge significantly. |
| Keywords: | private provision of public goods, GoBs, heterogeneity, externalities, free-riding, free-driving |
| JEL: | D01 D62 H23 H41 Q54 Q59 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11736 |
| By: | Baumgartner, Stefanie S. (University of Fribourg); Galeotti, Fabio (CNRS, GATE); Madies, Thierry (University of Fribourg); Villeval, Marie Claire (CNRS) |
| Abstract: | Trust plays a crucial role in refugees’ integration. This study examines how social information about trust levels among peers from home and host countries affects non-Western refugees’ trust. Using a trust game, we measured experimentally trust levels among Swiss citizens, Turkish refugees, and Afghan refugees. We found that Turkish refugees exhibited higher trust levels than Afghan refugees, but no significant trust differences were found between Swiss participants and either refugee group. Turkish refugees adjusted their trust to match Swiss levels when receiving social information, but observation by compatriots reduced this effect. By contrast, Afghan refugees exhibited a more limited response to social information, except when told their behavior would be revealed, which led them to align more closely with Swiss trust levels. These findings highlight the complex impact of social information on refugee trust behavior and suggest that trust can be a social norm. |
| Keywords: | refugees, trust, social information, lab-in-the-field experiment |
| JEL: | C91 D83 D91 F22 J61 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17822 |
| By: | Aaheli Ahmed; Sugata Marjit; Debashis Chakraborty |
| Abstract: | A major section of the existing literature on strategic trade policy, following a partial equilibrium framework, observed that imposition of tariff by the domestic country leads to a rise in their wage level. Analysis on the impact of strategic trade policy intervention (tariff) on wages and welfare in a two-country general oligopolistic equilibrium (GOLE) model framework in the current paper leads to a number of interesting results. First, imposition of tariff does not affect the wages in domestic country. In addition, the welfare of the tariff-imposing country unambiguously comes down. Second, a comparison of the revenue generated from tariff and the subsidy required to compensate the affected workers reveals that when only trade in final goods is allowed, such compensation is possible beyond a specific level of tariff rate, which is directly related to foreign tariff rate. In effect, a high value of foreign tariff implies a lower ability of the domestic government to subsidize the workers. Third, however, when trade in both final and intermediate goods take place, the opposite results emerge, where tariff revenue can compensate the workers up to a certain level of tariff rate. The underlying logic is that imposition of tariff may lead to a fall in the overall demand for workers in the domestic country. The results are of crucial policy relevance, especially given the increasing participation of developing countries in Global Value Chains (GVCs) and re-emergence of tariff protectionism in several countries. |
| Keywords: | Cournot Competition, tariff, wage, compensation, general oligopolistic equilibrium (GOLE), welfare |
| JEL: | D43 J33 L13 I31 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11707 |