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on Game Theory |
| By: | Srihari Govindan; Robert B. Wilson |
| Abstract: | A solution concept that is a refinement of Nash equilibria selects for each finite game a nonempty collection of closed and connected subsets of Nash equilibria as solutions. We impose three axioms for such solution concepts. The axiom of backward induction requires each solution to contain a quasi-perfect equilibrium. Two invariance axioms posit that solutions of a game are the same as those of a game obtained by the addition of strategically irrelevant strategies and players. Stability satisfies these axioms; and any solution concept that satisfies them must, for generic extensive-form games, select from among its stable outcomes. A strengthening of the two invariance axioms provides an analogous axiomatization of components of equilibria with a nonzero index. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.16908 |
| By: | Sam Ganzfried |
| Abstract: | Dominance is a fundamental concept in game theory. In strategic-form games dominated strategies can be identified in polynomial time. As a consequence, iterative removal of dominated strategies can be performed efficiently as a preprocessing step for reducing the size of a game before computing a Nash equilibrium. For imperfect-information games in extensive form, we could convert the game to strategic form and then iteratively remove dominated strategies in the same way; however, this conversion may cause an exponential blowup in game size. In this paper we define and study the concept of dominated actions in imperfect-information games. Our main result is a polynomial-time algorithm for determining whether an action is dominated (strictly or weakly) by any mixed strategy in n-player games, which can be extended to an algorithm for iteratively removing dominated actions. This allows us to efficiently reduce the size of the game tree as a preprocessing step for Nash equilibrium computation. We explore the role of dominated actions empirically in the "All In or Fold" No-Limit Texas Hold'em poker variant. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.09716 |
| By: | Denis Kojevnikov; Kyungchul Song |
| Abstract: | We consider incomplete information finite-player games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolutely continuous information in Milgrom and Weber (1985), and prove that a Bayesian equilibrium exists under broad conditions. Applying these results to games with rich type spaces that accommodate infinite belief hierarchies, we show that when the analyst's game has a type space satisfying absolute continuity of beliefs, the actual game played according to the belief hierarchies induced by the type space has a Bayesian equilibrium for a wide class of games. We provide examples that illustrate practical applications of our findings. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.16240 |
| By: | Jens Leth Hougaard (University of Copenhagen, DK-1958 Frederiksberg C, Denmark); Mich Tvede (School of Economics, University of Sheffield, Sheffield S1 4DT, UK) |
| Abstract: | We consider network formation. A set of locations can be connected in various network configurations. Every network has a cost and every agent has an individual value of every network. A planner aims at implementing a welfare maximizing network and allocating the resulting cost, but information is asymmetric: agents are fully informed and the planner is ignorant. Full implementation in Nash and strong Nash equilibria is studied. We show the correspondence consisting of welfare maximizing networks and individually rational cost allocations is implementable. We construct a minimal Nash implementable, welfare maximizing, and individually rational solution in the set of upper hemi-continuous and Nash implementable solutions. It is not possible to have full implementation single valued solutions such as the Shapley value. |
| Keywords: | Networks; Welfare maximization; Nash Implementation; Strong Nash Implementation |
| JEL: | C70 C72 D71 D85 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:shf:wpaper:2025005 |
| By: | Chowdhury Mohammad Sakib Anwar; Konstantinos Georgalos; Sonali SenGupta |
| Abstract: | Gallice and Monzon (2019) present a natural environment that sustains full cooperation in one-shot social dilemmas among a finite number of self-interested agents. They demonstrate that in a sequential public goods game, where agents lack knowledge of their position in the sequence but can observe some predecessors' actions, full contribution emerges in equilibrium due to agents' incentive to induce potential successors to follow suit. Furthermore, they show that this principle extends to a number of social dilemmas, with the prominent example that of the prisoner's dilemma. In this study, we experimentally test the theoretical predictions of this model in a multi- player prisoner's dilemma environment, where subjects are not aware of their position in the sequence and receive only partial information on past cooperating actions. We test the predictions of the model, and through rigorous structural econometric analysis, we test the descriptive capacity of the model against alternative behavioural strategies, such as conditional cooperation, altruistic play and free-riding behaviour. We find that the majority resorts to free-riding behaviour, around 30% is classified as Gallice and Monzon (2019) types, followed by those with social preference considerations and the unconditional altruists. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.10441 |
| By: | Takashi Izumo |
| Abstract: | In everyday life, we frequently make coarse-grained judgments. When we say that Olivia and Noah excel in mathematics, we disregard the specific differences in their mathematical abilities. Similarly, when we claim that a particular automobile manufacturer produces high-quality cars, we overlook the minor variations among individual vehicles. These coarse-grained assessments are distinct from erroneous or deceptive judgments, such as those resulting from student cheating or false advertising by corporations. Despite the prevalence of such judgments, little attention has been given to their underlying mathematical structure. In this paper, we introduce the concept of coarse-graining into game theory, analyzing games where players may perceive different payoffs as identical while preserving the underlying order structure. We call it a Coarse-Grained Game (CGG). This framework allows us to examine the rational inference processes that arise when players equate distinct micro-level payoffs at a macro level, and to explore how Nash equilibria are preserved or altered as a result. Our key findings suggest that CGGs possess several desirable properties that make them suitable for modeling phenomena in the social sciences. This paper demonstrates two such applications: first, in cases of overly minor product updates, consumers may encounter an equilibrium selection problem, resulting in market behavior that is not driven by objective quality differences; second, the lemon market can be analyzed not only through objective information asymmetry but also through asymmetries in perceptual resolution or recognition ability. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.17598 |
| By: | Aïd, René; Bonesini, Ofelia; Callegaro, Giorgia; Campi, Luciano |
| Abstract: | We frame dynamic persuasion in a partial observation stochastic control Leader-Follower game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver's value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that even in the absence of information cost, it might be optimal for the regulator to blur information available to firms to prevent them from coordinating on a higher level of carbon footprint to reduce their cost of reaching a below average emission target. |
| Keywords: | persuasion; filtering; ergodic control; Stackelberg games; mean field games; smart meters; carbon footprint |
| JEL: | C61 C73 D82 D83 Q51 |
| Date: | 2025–07–31 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:127889 |
| By: | Songtao He; Erfang Shan; Hanqi Zhou |
| Abstract: | The Owen value is an well-known allocation rule for cooperative games with coalition structure.In this paper, we introduce the concept of highly mutually dependent unions. Two unions in a cooperative game with coalition structure are said to be highly mutually dependent if any pair of players, with one from each of the two unions, are mutually dependent in the game.Based on this concept, we introduce two axioms: weak mutually dependent between unions and differential marginality of inter-mutually dependent unions. Furthermore, we also propose another two axioms: super inter-unions marginality and invariance across games, where the former one is based on the concept of the inter-unions marginal contribution. By using the axioms and combining with some standard axioms, we present three axiomatic characterizations of the Owen value. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.14230 |
| By: | Darpoe, Erik; Dominguez, Alvaro; Martin-Rodriguez, Maria |
| Abstract: | n a scenario featuring two distinct player types, we examine the pairwise stability of stationary networks where agents engage in infinite-horizon bargaining games akin to Manea's framework. Link formation and maintenance costs are contingent upon communication ease and complementarities, with connections between individuals of different types becoming less expensive when complementarities are sufficiently strong. In such instances, various bipartite components emerge as stable, characterized by a lack of direct connections between players of the same type. These components exhibit inequitable disributions of surplus, resulting in asymmetric splits among linked individuals. This contrasts with scenarios where connections between individuals of the same type are less costly, leading to predominantly equitable stable components. OUr findings highlight how complementarities and the relative scarcity of certain types can influence the fairness of bargaining outcomes within networks. |
| Keywords: | Bargaining, Heterogeneity, Networks, Pairwise stability |
| JEL: | C72 C78 D85 |
| URL: | https://d.repec.org/n?u=RePEc:agi:wpaper:02000085 |
| By: | Liam Welsh; Udit Grover; Sebastian Jaimungal |
| Abstract: | Climate change is a major threat to the future of humanity, and its impacts are being intensified by excess man-made greenhouse gas emissions. One method governments can employ to control these emissions is to provide firms with emission limits and penalize any excess emissions above the limit. Excess emissions may also be offset by firms who choose to invest in carbon reducing and capturing projects. These projects generate offset credits which can be submitted to a regulating agency to offset a firm's excess emissions, or they can be traded with other firms. In this work, we characterize the finite-agent Nash equilibrium for offset credit markets. As computing Nash equilibria is an NP-hard problem, we utilize the modern reinforcement learning technique Nash-DQN to efficiently estimate the market's Nash equilibria. We demonstrate not only the validity of employing reinforcement learning methods applied to climate themed financial markets, but also the significant financial savings emitting firms may achieve when abiding by the Nash equilibria through numerical experiments. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.11258 |
| By: | Stephen Martin |
| Abstract: | The paper analyzes a two-stage Main Street model. In the second stage, taking locations as given, each of two firms sets price to maximize own profit, subject to the constraint that it is not profitable for the other firm to undercut its price at its location. We find constrained price best-response equations and pure-strategy equilibrium prices for all pairs of locations. In the first stage, firms noncooperatively pick locations to maximize second-stage payoffs. We find location best-response equations and equilibrium locations. Equilibrium locations are efficient in the sense of minimizing transportation cost. |
| Keywords: | Main Street, Hotelling, price undercutting |
| JEL: | C72 D21 D43 L13 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:pur:prukra:1354 |
| By: | Ohnishi, Kazuhiro |
| Abstract: | An existing study examines an international mixed duopoly involving a state-owned public firm and a foreign private firm, focusing on their timing choices for quantities and showing that the state-owned public firm should act as the leader. This result differs from that for an endogenous-timing mixed duopoly model where a state-owned public firm coexists with a domestic private firm. We investigate the endogenous order of moves in a mixed duopoly model where a state-owned public firm competes with a private firm that is partially foreign-owned. Specifically, we explore the desirable role of the state-owned public firm, either as a leader or a follower, and present the equilibrium outcome of the model. Our findings reveal that the equilibrium differs depending on whether the foreign ownership ratio of the private firm is low or high. |
| Keywords: | Endogenous timing; Mixed oligopoly; Partial foreign ownership; Stackelberg |
| JEL: | C72 D21 F23 L13 L32 |
| Date: | 2025–05–02 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:124662 |
| By: | Florian Brandl |
| Abstract: | We consider long-lived agents who interact repeatedly in a social network. In each period, each agent learns about an unknown state by observing a private signal and her neighbors' actions in the previous period before taking an action herself. Our main result shows that the learning rate of the slowest learning agent is bounded from above independently of the number of agents, the network structure, and the agents' strategies. Applying this result to equilibrium learning with rational agents shows that the learning rate of all agents in any equilibrium is bounded under general conditions. This extends recent findings on equilibrium learning and demonstrates that the limitation stems from an inherent tradeoff between optimal action choices and information revelation rather than strategic considerations. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.12136 |
| By: | Luke Boosey; Philip Brookins; Dmitry Ryvkin |
| Abstract: | We study information disclosure policies for contests among groups. Each player endogenously decides whether or not to participate in competition as a member of their group. Within-group aggregation of effort is best-shot, i.e., each group's performance is determined by the highest investment among its members. We consider a generalized all-pay auction setting, in which the group with the highest performance wins the contest with certainty. Players' values for winning are private information at the entry stage, but may be disclosed at the competition stage. We compare three disclosure policies: (i) no disclosure, when the number of entrants remains unknown and their values private; (ii) within-group disclosure, when this information is disclosed within each group but not across groups; and (iii) full disclosure, when the information about entrants is disclosed across groups. For the benchmark case of contests between individuals, information disclosure always reduces expected aggregate investment. However, this is no longer true in group contests: Within-group disclosure unambiguously raises aggregate investment, while the effect of full disclosure is ambiguous. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.20092 |
| By: | Yiyin Cao; Chuangyin Dang |
| Abstract: | Sequential equilibrium requires a consistent assessment and sequential rationality, where the consistent assessment emerges from a convergent sequence of totally mixed behavioral strategies and associated beliefs. However, the original definition lacks explicit guidance on constructing such convergent sequences. To overcome this difficulty, this paper presents a characterization of sequential equilibrium by introducing $\varepsilon$-perfect $\gamma$-sequential equilibrium with local sequential rationality. For any $\gamma>0$, we establish a perfect $\gamma$-sequential equilibrium as a limit point of a sequence of $\varepsilon_k$-perfect $\gamma$-sequential equilibrium with $\varepsilon_k\to 0$. A sequential equilibrium is then derived from a limit point of a sequence of perfect $\gamma_q$-sequential equilibrium with $\gamma_q\to 0$. This characterization systematizes the construction of convergent sequences and enables the analytical determination of sequential equilibria and the development of a polynomial system serving as a necessary and sufficient condition for $\varepsilon$-perfect $\gamma$-sequential equilibrium. Exploiting the characterization, we develop a differentiable path-following method to compute a sequential equilibrium. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.19493 |
| By: | Aid, René (Center for Mathematical Economics, Bielefeld University); Federico, Salvatore (Center for Mathematical Economics, Bielefeld University); Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University); Rodosthenous, Neofytos (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study the problem of optimal investment in brown (carbon-intensive) production amid climate change and the impact of rising global temperatures. Our approach is based on a mean-field model of firms that produce goods whose productivity is adversely affected by temperature-related damages, which are in turn linked to the global stock of greenhouse gas (GHG) emissions. Each firm controls its investment rate in view of increasing its capital stock, which evolves stochastically due to idiosyncratic Gaussian shocks and is subject to exponential depreciation in the absence of investment. Firms aim to maximize their expected discounted profits, net of investment costs, by choosing investment strategies that respond to the level of aggregate GHG emissions and their adverse impact. We constructively establish the existence and uniqueness of a mean-field equilibrium, by characterising it as the unique solution to a bespoke three-dimensional system of forward-backward ordinary differential equations. This characterisation enables the implementation of the model to support numerical analyses for exploring the implications of climate damage on equilibrium outcomes and policy design in terms of taxes and phase-out dates for brown production. |
| Keywords: | mean-field games, climate change, optimal investment, mean-field equilibrium, forward-backward ODEs |
| Date: | 2025–05–13 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:705 |
| By: | Ben D'Exelle; Christine Gutekunst; Arno Riedl |
| Abstract: | We conduct an artefactual field experiment in real-existing trade networks to analyze how individual network degree affects bargaining demands and outcomes. We combine data from a bilateral bargaining experiment with data of trade networks in 24 villages in Uganda. To identify the effect of individual degree in the village trade network we experimentally vary the disclosure of participants’ identities in a bargaining pair. We derive hypotheses on how degree should affect behavior and find partial support for them. Specifically, we observe that individual degree affects bargaining demands in the predicted direction when one of the bargainers is informed about the network positions but not when both sides are informed. Moreover, network degree affects the likelihood of agreements and earnings, irrespective of the knowledge of the network positions of bargaining partners. |
| Keywords: | bargaining, social networks, network degree, experiments. |
| JEL: | C78 C90 L14 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11832 |
| By: | Gurkirat Wadhwa; Veeraruna Kavitha |
| Abstract: | Considering a supply chain with partial vertical integration, we attempt to seek answers to several questions related to the cooperation competition based friction, abundant in such networks. Such an SC can represent a supplier with an inhouse production unit that attempts to control an outhouse production unit via the said friction. The two production units can have different sets of loyal customer bases and the aim of the manufacturer supplier duo would be to get the best out of the two customer bases. Our analysis shows that under certain market conditions, an optimal strategy might be to allow both units to earn positive profits particularly when they hold similar market power and when customer loyalty is high. In cases of weaker customer loyalty, however, the optimal approach may involve pressurizing the outhouse unit to operate at minimal profits. Even more intriguing is the scenario where the outhouse unit has a greater market power and customer loyalty remains strong here, it may be optimal for the inhouse unit to operate at a loss just enough to dismantle the downstream monopoly. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.09591 |
| By: | Rey, Patrick; Loertscher, Simon; Marx, Leslie |
| Abstract: | We develop the procurement analogue to an all-pay auction for an independent private values model with identical distributions. In this all-receive procurement auction (ARPA), suppliers simultaneously submit bids. Suppliers with bids below (above) the reserve are paid their bids (are paid and produce nothing). The supplier with the largest bid below the reserve produces the good. With appropriately chosen reserves, which decrease in the number of suppliers, the ARPA is efficient and, given increasing virtual costs, implements the optimal procurement. Appropriately adjusted, ARPAs implement the optimal procurement in general. ARPAs can render supply chains resilient to nonanticipated liquidity shocks. |
| Keywords: | Resilience; Liquidity shocks; All-pay auctions; Multiple-receive procurement auctions |
| JEL: | D44 D82 L41 |
| Date: | 2025–04–29 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130525 |
| By: | Elena Prager; Nicholas Tilipman |
| Abstract: | Recent policy proposals seek to regulate out-of-network hospital prices. We study how such regulation affects equilibrium prices, network formation, and hospital exit. We estimate a structural model of insurer-hospital bargaining that allows for out-of-network transactions between non-contracting parties. These transactions generate a notion of exit by rendering hospitals unprofitable under some regulations. Estimation relies on a novel measure of out-of-network prices. We find that reducing out-of-network prices would also lower negotiated prices, but potentially at the cost of narrower hospital networks. Aggressive regulation could induce substantial hospital exit, but only under the restrictive assumption that negotiators cannot anticipate the exits. |
| JEL: | C78 I11 L13 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:33727 |
| By: | Jing Jing Li (Centre for Health Economics, Monash Business School, Monash University); Anthony Harris (Centre for Health Economics, Monash Business School, Monash University) |
| Abstract: | Public funding decisions for pharmaceuticals are the outcomes of a dynamic bilateral bargaining process between the funding agency and a company and can involve considerable delay. Using an empirical duration model of negotiation in Australia from 2005 to 2018, we test if agreement patterns on national public subsidy of pharmaceuticals are consistent with the predictions of dynamic bargaining theory. It took a median of 16 months for the Australian government and companies to reach an agreement, averaging 1.51 rounds of negotiations, with 71% of the rounds failing to reach an agreement. Overall, the results of a process of one- sided offers from companies are consistent with theories of bargaining with incomplete information and delay strategies, where evidence of quality develops over negotiation rounds. Lower value and more risk for the payer delayed agreements and increased the probability of no agreement, while public awareness and interest in a drug reduced the agency’s bargaining power and increased agreement rates. Enhanced knowledge about the drug’s attributes benefits the government and its constituencies, but pharmaceutical companies have a strong incentive to invest in political alliances to raise awareness of potential benefits to patients and hasten public funding of a drug. |
| Keywords: | dynamic bargaining, pharmaceuticals, drug funding |
| JEL: | I11 H51 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:mhe:chemon:2025-09 |
| By: | Cremer, Helmuth; Borsenberger, Claire; Joram, Denis; Lozachmeur, Jean-Marie; Malavolti, Estelle |
| Abstract: | The concept of Corporate Social Responsibility (CSR) has evolved since Milton Friedman’s 1970 assertion that a business’s sole responsibility is profit. Today, global frameworks like the UN Global Compact and EU regulations emphasize corporate accountability, particularly regarding social and environmental impacts. Corporate Social Responsibility (CSR) has become central in discussions of firm behavior, governance, and public goods provision. CSR however varies across firms. Some adopt basic strategic CSR (b-CSR), considering social and environmental issues only to the extent that they affect consumer demand and profitability. Others practice environmentally committed CSR (e-CSR), internalizing the full social cost of emissions. A few pursue fully committed CSR (w-CSR), aiming to maximize overall social welfare. The paper analyzes CSR’s effects on firm behavior through economic modeling. It first examines a single firm producing CO2 emissions, where reducing emissions increases costs but appeals to environmentally conscious consumers. Three firm types—b-CSR, e-CSR, and w-CSR—are considered. The study then extends to a competitive market with two firms engaged in Cournot competition. It examines scenarios where firms have different CSR commitments, analyzing how competition, emissions, and profits are affected. Finally, the paper compares these outcomes to an ideal scenario where firms are regulated to maximize social welfare. |
| Keywords: | Motivation and sustainability of CSR under competition; mission oriented; firms, consumers’ environmental awareness and profit maximization; differentiated duopoly; duopoly. |
| JEL: | H23 L13 L31 G50 |
| Date: | 2025–05–02 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130533 |
| By: | Fuhito Kojima; Bobak Pakzad-Hurson |
| Abstract: | We study a variation of the price competition model a la Bertrand, in which firms must offer menus of contracts that obey monotonicity constraints, e.g., wages that rise with worker productivity to comport with equal pay legislation. While such constraints limit firms' ability to undercut their competitors, we show that Bertrand's classic result still holds: competition drives firm profits to zero and leads to efficient allocations without rationing. Our findings suggest that Bertrand's logic extends to a broader variety of markets, including labor and product markets that are subject to real-world constraints on pricing across workers and products. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.16842 |