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on Game Theory |
| By: | Bailey, Ralph W. (Department of Economics, University of Birmingham, UK); Kozlovskaya, Maria (Economics, Finance and Entrepreneurship Department, Aston Business School, Aston University, UK); Ray, Indrajit (Cardiff Business School, Cardiff University) |
| Abstract: | We study mixed-strategy equilibria in a two-good buy-and-sell strategic market game à la Shapley–Shubik. We show that expected utility need not be quasiconcave in strategies, creating difficulties for characterising mixed equilibria. We prove that any mixed Nash profile in which each player mixes over only two positive bids is purifiable and the implied outcome is a mixture over pure equilibria. |
| Keywords: | Mixed bids; Mixed strategy Nash equilibrium; Strategic market games |
| JEL: | C72 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2025/21 |
| By: | Hideo Konishi (Boston College); Michel Le Breton (Toulouse School of Economics); Shlomo Weber (Southern Methodist University) |
| Abstract: | In this paper, we define additive dyadic social interactions games (ADG), in which each player cares not only about the selected action, but also about interactions with other players, especially those who choose the same action. This class of games includes alliance formation games, network games, and dis- crete choice problems with network externalities. While it is known that games in the ADG class admit a pure strategy Nash equilibrium that is a maximizer of the game's potential, the potential approach does not always apply if all coalitional deviations are allowed. We then introduce a novel notion of a strong landscape equilibrium, which relies on a limited scope of coalitional deviations. We show the existence of a strong landscape equilibrium for a class of basic additive dyadic social interactions games (BADG), even though a strong Nash equilibrium may fail to exist. Somewhat surprisingly, a potential-maximizing strong landscape equilibrium is not always a strong Nash equilibrium even if the set of the latter is nonempty. We also provide applications and extensions of our results. |
| Keywords: | social interactions games, coalition, landscape equilibrium |
| Date: | 2025–10–25 |
| URL: | https://d.repec.org/n?u=RePEc:boc:bocoec:1098 |
| By: | Shuige Liu; Gabriel Ziegler |
| Abstract: | Interactive decision-making relies on strategic reasoning. Two prominent frameworks capture this idea. One follows a structural perspective, exemplified by level-k and Cognitive Hierarchy models, which represent reasoning as an algorithmic process. The other adopts an epistemic perspective, formalizing reasoning through beliefs and higher-order beliefs. We connect these approaches by "Lifting" static complete-information games into incomplete-information settings where payoff types reflect players' levels. Within this unified framework, reasoning is represented through mathematically explicit and transparent belief restrictions. We analyze three instances: downward rationalizability, a robust benchmark concept; and two refinements, L-rationalizability and CH-rationalizability, which provide epistemic foundations---albeit with a nuance---for the classic level-k and Cognitive Hierarchy models, respectively. Our results clarify how reasoning depth relates to behavioral predictions, distinguish cognitive limits from belief restrictions, and connect bounded reasoning to robustness principles from mechanism design. The framework thus offers a transparent and tractable bridge between structural and epistemic approaches to reasoning in games. |
| Keywords: | bounded reasoning, behavioral game theory, level-k, cognitive hierarchy, epistemic game theory, belief restrictions, Δ-rationalizability, robustness |
| JEL: | C72 D82 D83 D90 |
| Date: | 2025–10–20 |
| URL: | https://d.repec.org/n?u=RePEc:bdp:dpaper:0079 |
| By: | Bhunia, Soumyajit |
| Abstract: | Game theory offers a structured framework for analyzing strategic decision making. This paper is trying to examine strategic decision-making in cricket, where both the teams aim to maximize their outcomes in a competitive environment. By examining payoffs, probabilities, and opponent strategies, we investigate the interplay between possible risk and reward, bolstering to more informed and effective tactics in the match. |
| Keywords: | strategic decision, cricket, pay-offs, risk |
| JEL: | A1 C7 C70 Y1 |
| Date: | 2025–01–06 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126153 |
| By: | Rubik Khachatryan; Georgy Lukyanov |
| Abstract: | We analyze a two-period, two-market chain-store game in which an incumbent's conduct in one market is only sometimes seen in the other. This partial observability generates reputational spillovers across markets. We characterize equilibrium behavior by prior reputation: at high priors the strategic incumbent fights a lone early entrant (and mixes when both arrive together); at low priors it mixes against a single entrant and accommodates coordinated entry. Greater observability increases early fighting yet, because any accommodation is more widely noticed, raises the incidence of later entry. The results are robust to noisy signals and endogenous information acquisition, and extend naturally to many markets. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.21759 |
| By: | Sumit Goel; Yiqing Yan; Jeffrey Zeidel |
| Abstract: | We study the effect of interim feedback policies in a dynamic all-pay auction where two players bid over two stages to win a common-value prize. We show that sequential equilibrium outcomes are characterized by Cheapest Signal Equilibria, wherein stage 1 bids are such that one player bids zero while the other chooses a cheapest bid consistent with some signal. Equilibrium payoffs for both players are always zero, and the sum of expected total bids equals the value of the prize. We conduct an experiment with four natural feedback policy treatments -- full, rank, and two cutoff policies -- and while the bidding behavior deviates from equilibrium, we fail to reject the hypothesis of no treatment effect on total bids. Further, stage 1 bids induce sunk costs and head starts, and we test for the resulting sunk cost and discouragement effects in stage 2 bidding. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.23178 |
| By: | Fabian Raoul Pieroth; Ole Petersen; Martin Bichler |
| Abstract: | Predatory pricing -- where a firm strategically lowers prices to undermine competitors -- is a contentious topic in dynamic oligopoly theory, with scholars debating practical relevance and the existence of predatory equilibria. Although finite-horizon dynamic models have long been proposed to capture the strategic intertemporal incentives of oligopolists, the existence and form of equilibrium strategies in settings that allow for firm exit (drop-outs following loss-making periods) have remained an open question. We focus on the seminal dynamic oligopoly model by Selten (1965) that introduces the subgame perfect equilibrium and analyzes smooth market sharing. Equilibrium can be derived analytically in models that do not allow for dropouts, but not in models that can lead to predatory pricing. In this paper, we leverage recent advances in deep reinforcement learning to compute and verify equilibria in finite-horizon dynamic oligopoly games. Our experiments reveal two key findings: first, state-of-the-art deep reinforcement learning algorithms reliably converge to equilibrium in both perfect- and imperfect-information oligopoly models; second, when firms face asymmetric cost structures, the resulting equilibria exhibit predatory pricing behavior. These results demonstrate that predatory pricing can emerge as a rational equilibrium strategy across a broad variety of model settings. By providing equilibrium analysis of finite-horizon dynamic oligopoly models with drop-outs, our study answers a decade-old question and offers new insights for competition authorities and regulators. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.27008 |
| By: | Holmberg, P.; Ruddell, K.; Willems, B. |
| Abstract: | We characterize Nash equilibria in multi-product markets in which producers commit to vectors of supply functions contingent on all prices. The framework accommodates (dis)economies of scope in production, and goods may be substitutes or complements in demand. We show that equilibrium allocations of underlying goods and payoffs are invariant under bundling. With quadratic costs and linear demand, this invariance reduces the multi-product problem to an equivalent set of single-product markets that can be analyzed independently. We introduce Lerner and pass-through matrices to capture markups and welfare losses; their eigenvalues summarize fundamental market properties, remain invariant under bundling, and lend themselves to comparative statics analysis. |
| Keywords: | Supply Function Equilibrium, Multi-Product Pricing, Divisible-Good Auction, Bundling, Pass-Through, Welfare |
| JEL: | C62 C72 D43 D44 L94 |
| Date: | 2025–09–24 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camdae:2565 |
| By: | Volker Benndorf; Dorothea Kübler; Hans-Theo Normann |
| Abstract: | Information unraveling is an elegant theoretical argument suggesting that private information is voluntarily and fully revealed in many circumstances. However, the experimental literature has documented many cases of incomplete unraveling and has suggested limited depth of reasoning on the part of senders as a behavioral explanation. To test this explanation, we modify the design of existing unraveling games along two dimensions. In contrast to the baseline setting with simultaneous moves, we introduce a variant where decision-making is essentially sequential. Second, we vary the cost of disclosure, resulting in a 2x2 treatment design. Both sequential decision-making and low disclosure costs are suitable for reducing the demands on subjects' level-k reasoning. The data confirm that sequential decision-making and low disclosure costs lead to more disclosure, and there is virtually full disclosure in the treatment that combines both. A calibrated level-k model makes quantitative predictions, including precise treatment level and player-specific revelation rates, and these predictions organize the data well. The timing of decisions provides further insights into the treatment-specific unraveling process. |
| Keywords: | information revelation, level-k reasoning, sequential decisions, calibration |
| JEL: | C72 C90 C91 |
| Date: | 2025–10–20 |
| URL: | https://d.repec.org/n?u=RePEc:bdp:dpaper:0078 |
| By: | Gustavo Berganti\~nos; Juan D. Moreno-Ternero |
| Abstract: | We study the problem of measuring the popularity of artists in music streaming platforms and the ensuing methods to compensate them (from the revenues platforms raise by charging users). We uncover the space of popularity indices upon exploring the implications of several axioms capturing principles with normative appeal. As a result, we characterize several families of indices. Some of them are intimately connected to the Shapley value, the central tool in cooperative game theory. Our characterizations might help to address the rising concern in the music industry to explore new methods that reward artists more appropriately. We actually connect our families to the new royalties models, recently launched by Spotify and Deezer. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.25275 |
| By: | Pau Juan-Bartroli; Esteban Mu\~noz-Sobrado |
| Abstract: | The sustainability of cooperation is crucial for understanding the progress of societies. We study a repeated game in which individuals decide the share of their income to transfer to other group members. A central feature of our model is that individuals may, with some probability, switch incomes across periods, our measure of income mobility, while the overall income distribution remains constant over time. We analyze how income mobility and income inequality affect the sustainability of contribution norms, informal agreements about how much each member should transfer to the group. We find that greater income mobility facilitates cooperation. In contrast, the effect of inequality is ambiguous and depends on the progressivity of the contribution norm and the degree of mobility. We apply our framework to an optimal taxation problem to examine the interaction between public and private redistribution. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.26503 |
| By: | Cecilia Carvalho; Daniel Monte; Emanuel Ornelas |
| Abstract: | Members of the World Trade Organization are increasingly disregarding its rules, raising concerns about the future of the multilateral trading system. To analyze the sustainability of the rules-based trade regime, we develop a dynamic framework of stochastic asynchronous games where the leading country determines the trade regime and leadership changes over time. We show that transitioning from a power-based to a rules-based regime requires the presence of a hegemonic power â€" i.e., a country significantly larger than all others. Nonhegemonic leading countries benefit from a power-based regime, but may nevertheless uphold rules anticipating that they can lose their dominance in the future. We find that the longterm viability of a rules-based equilibrium hinges on the cost of establishing it, which must be neither too small nor too large, on countries’ discount factors and on the degree of turnover in world leadership, both of which must be sufficiently large. In a bipolar state, free-riding and market-power forces further undermine the feasibility of rules-based equilibria. We also highlight the trade-offs that a redesign of the WTO rules must face to remain viable. If the leading country becomes shortsighted, the system needs to become more efficient, offer more latitude to the leading country, or even exclude it from the system. |
| Keywords: | hegemonic stability theory, World Trade Organization, trade agreements |
| Date: | 2025–10–22 |
| URL: | https://d.repec.org/n?u=RePEc:cep:cepdps:dp2128 |
| By: | Daisuke Hirota |
| Abstract: | Cooperative systems often remain in persistently suboptimal yet stable states. This paper explains such "rational stagnation" as an equilibrium sustained by a rational adversary whose utility follows the principle of potential loss, $u_{D} = U_{ideal} - U_{actual}$. Starting from the Prisoner's Dilemma, we show that the transformation $u_{i}' = a\, u_{i} + b\, u_{j}$ and the ratio of mutual recognition $w = b/a$ generate a fragile cooperation band $[w_{\min}, \, w_{\max}]$ where both (C, C) and (D, D) are equilibria. Extending to a dynamic model with stochastic cooperative payoffs $R_{t}$ and intervention costs $(C_{c}, \, C_{m})$, a Bellman-style analysis yields three strategic regimes: immediate destruction, rational stagnation, and intervention abandonment. The appendix further generalizes the utility to a reference-dependent nonlinear form and proves its stability under reference shifts, ensuring robustness of the framework. Applications to social-media algorithms and political trust illustrate how adversarial rationality can deliberately preserve fragility. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.22232 |
| By: | Pau Juan-Bartroli; Jos\'e Ignacio Rivero-Wildemauwe |
| Abstract: | Rejections of positive offers in the Ultimatum Game have been attributed to different motivations. We show that a model combining social preferences and moral concerns provides a unifying explanation for these rejections while accounting for additional evidence. Under the preferences considered, a positive degree of spite is a necessary and sufficient condition for rejecting positive offers. This indicates that social preferences, rather than moral concerns, drive rejection behavior. This does not imply that moral concerns do not matter. We show that rejection thresholds increase with individuals' moral concerns, suggesting that morality acts as an amplifier of social preferences. Using data from van Leeuwen and Alger (2024), we estimate individuals' social preferences and moral concerns using a finite mixture approach. Consistent with previous evidence, we identify two types of individuals who reject positive offers in the Ultimatum Game, but that differ in their Dictator Game behavior. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.22086 |
| By: | Batabyal, Amitrajeet |
| Abstract: | We study the merits of regulating water pollution in the Ganges river caused by tanneries in Kanpur, India, by unitizing or merging the polluting tanneries. We first describe the � ≥ 2 polluting tanneries in Kanpur as a Cournot oligopoly in which all tanneries incur fixed and variable costs in producing leather. Second, we derive the Nash equilibrium output of leather and profits and discuss how many tanneries can survive in this equilibrium as a function of the fixed costs. Third, we permit � |
| Keywords: | Fixed Cost, Ganges River, Tannery, Unitization, Water Pollution |
| JEL: | G34 Q25 |
| Date: | 2025–02–15 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126501 |
| By: | Kamei, Kenju; Tabero, Katy |
| Abstract: | It is well-known that efficiency often fails to improve in public goods games with peer-to-peer punishment when counter-punishment is possible. This paper experimentally demonstrates, for the first time, that the effects of sanctioning institutions are modest, regardless of the decision-making format (individual or team). In the “team” conditions, subjects are randomly assigned to teams of three, and make joint decisions through communication. Their dialogue provides valuable insights into the motivations behind (counter-)punishment, as well as the resulting behavioral effects. A coding exercise reveals that first-order punishments (and counter-punishments) are primarily emotional responses to peers’ low contributions (and first-order punishments, respectively). |
| Keywords: | C92, D01, H49 |
| JEL: | C92 D01 H41 H49 |
| Date: | 2025–09–03 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126063 |
| By: | Ohnishi, Kazuhiro |
| Abstract: | We employ a game-theoretic model to analyze five duopoly regimes: (1) state-owned and labor-managed firms, (2) labor-managed firms, (3) state-owned and capitalist firms, (4) capitalist firms, and (5) capitalist and labor-managed firms. We compare the welfare outcomes across these regimes and find that labor-managed firms may not be socially desirable due to their adverse impact on economic welfare. This may help explain why labor-managed firms are relatively rare compared to capitalist firms. |
| Keywords: | Capitalist firm; Cournot model; Economic welfare; Labor-managed firms; State-owned firm |
| JEL: | C72 D21 L32 |
| Date: | 2025–09–15 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126158 |
| By: | Yukihiko Funaki; Yukio Koriyama; Satoshi Nakada |
| Abstract: | Some well-known solutions for cooperative games with transferable utility (TU-games), such as the Banzhaf value, the Myerson value, and the Aumann-Dreze value, fail to satisfy efficiency, although they possess other desirable properties. This paper proposes a new approach to restore efficiency by extending any underlying solution to an efficient one, through what we call an efficient extension operator. We consider novel axioms for an efficient extension operator and characterize the egalitarian surplus sharing method and the proportional sharing method in a unified manner. These results can be considered as new justifications for the f-ESS values and the f-PS values introduced by Funaki and Koriyama (2025), which are generalizations of the equal surplus sharing value and the proportional sharing value. Our results offer an additional rationale for the values with an arbitrary underlying solution. As applications, we develop an efficient-fair extension of the solutions for the TU-games with communication networks and its variant for TU-games with coalition structures. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.24388 |
| By: | Pablo Brañas-Garza (Universidad Loyola Andalucía); Antonio M. Espín (Universidad de Granada); Diego Jorrat (Universidad de Sevilla/Loyola Behavioral Lab) |
| Abstract: | We conducted an online Dictator Game experiment (N = 1, 195) to test three hypotheses about the role of monetary incentives in prosocial behavior. First, we examined whether real incentives reduce the dispersion of responses compared to hypothetical ones. Surprisingly, we found the opposite: hypothetical responses were less dispersed, with choices clustering around the egalitarian split. This pattern held in a replication (N = 308) with higher stakes (£5), offering no support for the first hypothesis. Second, we tested whether real incentives—by involving actual monetary consequences—lead to more selfish decisions, as they are expected to reveal true preferences. With £1 stakes, no significant differences emerged across conditions. However, when the stake was increased to £5, participants became more selfish under real incentives, supporting the second hypothesis only when the amount at stake is substantial. Third, we explored whether probabilistic payments differ behaviorally from certain ones. At low stakes, probabilistic incentives resembled real ones. But with higher stakes, real and probabilistic outcomes diverged, suggesting participants respond to expected value only when it is meaningful. Finally, in a separate study (N = 299), we found that many participants misunderstood hypothetical-payment instructions. Only explicit phrasing eliminated this confusion, underscoring the importance of precise wording in experimental design. |
| Keywords: | Monetary incentives, egalitarianism, hyper-altruism, selfishness, dictator game |
| JEL: | D64 D91 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:aoz:wpaper:376 |
| By: | Yuchao Dong; Harry Zheng |
| Abstract: | This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing regularization method: first, we introduce an entropy-based regularization term to the MV objective, modeling mixed-strategy stopping times using the intensity of a Cox process. For this regularized problem, we derive a coupled extended Hamilton-Jacobi-Bellman (HJB) equation system, prove a verification theorem linking its solutions to equilibrium intensities, and establish the existence of classical solutions for small time horizons via a contraction mapping argument. By letting the regularization term tend to zero, we formally recover a system of parabolic variational inequalities that characterizes equilibrium stopping times for the original MV problem. This system includes an additional key quadratic term--a distinction from classical optimal stopping, where stopping conditions depend only on comparing the value function to the instantaneous reward. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.24128 |