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on Game Theory |
| By: | Rajdeep Tah; Colin Benjamin |
| Abstract: | Consider the scenario where an infinite number of players (i.e., the \textit{thermodynamic} limit) find themselves in a Prisoner's dilemma type situation, in a \textit{repeated} setting. Is it reasonable to anticipate that, in these circumstances, cooperation will emerge? This paper addresses this question by examining the emergence of cooperative behaviour, in the presence of \textit{noise} (or, under \textit{selection pressure}), in repeated Prisoner's Dilemma games, involving strategies such as \textit{Tit-for-Tat}, \textit{Always Defect}, \textit{GRIM}, \textit{Win-Stay, Lose-Shift}, and others. To analyze these games, we employ a numerical Agent-Based Model (ABM) and compare it with the analytical Nash Equilibrium Mapping (NEM) technique, both based on the \textit{1D}-Ising chain. We use \textit{game magnetization} as an indicator of cooperative behaviour. A significant finding is that for some repeated games, a discontinuity in the game magnetization indicates a \textit{first}-order \textit{selection pressure/noise}-driven phase transition. The phase transition is particular to strategies where players do not severely punish a single defection. We also observe that in these particular cases, the phase transition critically depends on the number of \textit{rounds} the game is played in the thermodynamic limit. For all five games, we find that both ABM and NEM, in conjunction with game magnetization, provide crucial inputs on how cooperative behaviour can emerge in an infinite-player repeated Prisoner's dilemma game. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.15801 |
| By: | Gill, David (Purdue University); Knepper, Zachary (Purdue University); Prowse, Victoria L. (Purdue University); Zhou, Junya (University of Texas at Dallas) |
| Abstract: | We explore the influence of cognitive ability and judgment on strategic behavior in the beauty contest game (where the Nash equilibrium action is zero). Using the level-k model of bounded rationality, cognitive ability and judgment both predict higher level strategic thinking. However, individuals with better judgment choose zero less frequently, and we uncover a novel dynamic mechanism that sheds light on this pattern. Taken together, our results indicate that fluid (i.e., analytical) intelligence is a primary driver of strategic level-k thinking, while facets of judgment that are distinct from fluid intelligence drive the lower inclination of high judgment individuals to choose zero. |
| Keywords: | cognitive ability, judgment, fluid intelligence, matrix reasoning, beauty contest, strategic sophistication, level-k, experiment, game theory |
| JEL: | C92 C72 D91 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17168 |
| By: | Ohnishi, Kazuhiro |
| Abstract: | This paper explores a price-setting oligopoly game where labor-managed firms have the option to provide lifetime employment as a strategic commitment. The game unfolds in two stages. In the first stage, each firm independently and simultaneously decides whether to provide lifetime employment as a strategic commitment. If a firm provides lifetime employment, then it chooses an output level and establishes a lifetime employment agreement with the required number of employees to reach the output level. In the second stage, each firm independently and simultaneously selects a price level to maximize its objective function value. At the conclusion of the second stage, the market opens, and each firm sells at its own price. The paper delves into the equilibrium of the labor-managed Bertrand oligopoly game. The analysis reveals that the equilibrium aligns with the Bertrand solution when no lifetime employment is offered. Consequently, the paper concludes that using lifetime employment as a strategic commitment device is not advantageous for labor-managed firms in the price-setting competition. |
| Keywords: | Labor-managed firm; Lifetime employment; Price-setting model; Substitute goods |
| JEL: | C72 D21 L13 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121486 |
| By: | Ghorbani, Khashayar |
| Keywords: | Health Economics And Policy |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea22:344031 |
| By: | Sharma, Shashidharan |
| Abstract: | This paper aims to address a gap in literature at the intersection of cheating in auctions and emotional responses. In a second price auction with a cheating seller, we model the bidder's dislike for the possibility of cheating by drawing upon the idea of reference point-based utility. A symmetric increasing equilibrium strategy is characterised and comparative statics are analysed. A comparison of expected payoffs to honest and dishonest sellers is made. We find that if reference points are low enough then the cheating seller's payoff is lower than what a seller earns in a regular first-price auction. Our results show that even with bidders disliking cheating, honest sellers lose out due to bidders shading their bids to accommodate for the possibility of being cheated. |
| Keywords: | Second Price Auctions, Reference Dependence, Emotional Responses |
| JEL: | D44 D89 |
| Date: | 2022–12–27 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121492 |
| By: | Paul Beaudry; Dana S. Galizia; Franck Portier |
| Abstract: | Macroeconomic dynamics are shaped by how individual incentives to spend and accumulate interact with the decisions of others. The goal of this paper is to identify—within a simple large-game-theoretic structure—which types of agent interactions favor which types of dynamic equilibrium outcomes. In particular, we extend the static analysis of Cooper and John 1988 to a dynamic setting to clarify the role of strategic complementarity and substitutability in delivering dynamics such as monotonic convergence to a unique steady state, hysteresis, endogenous cycles, and indeterminacy. |
| JEL: | E0 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32661 |
| By: | Sidarth Erat |
| Abstract: | The Colonel Blotto game, introduced by Borel in the 1920s, is often used for modeling various real-life settings, such as elections, lobbying, etc. The game is based on the allocation of limited resources by players to a set of fields. Each field is ``won'' and a corresponding field-specific value is obtained by the player who sends the most resources. In this paper, we formulate a discrete Blotto game played on a general \textit{accessibility network} (i.e., the bipartite graph made of players and the fields they can allocate resources to). The primary goal is to find how the topology of the accessibility network controls the existence and uniqueness of equilibrium allocations, and how it affects the fraction of fields that are entered and the average payoff of players at equilibrium. We establish that, in a 2-regular topology, when the values of fields are close enough and the number of players is not a multiple of 4, then there is a unique equilbrium. We also prove that players are better off and fields are more likely to be entered in a regular topology than a random topology. We find numerically that dispersion of field weights negatively affects average player payoff. The main contribution is a framework for analyzing contests where players are permitted access to some (but not necessarily all) venues of competition. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.16707 |
| By: | Guerrazzi, Marco |
| Abstract: | In this paper, I explore the relationship between wage bargaining and capital accumulation by developing a differential game in which a monopolistic union sets the wage of its members by taking as given the optimal employment strategy of a representative firm and the way in which capital is evaluated over time. Under the assumption that investment amounts to a constant share of produced output, I show that a meaningful open-loop Stackelberg equilibrium requires the union to be more patient than the firm. Moreover, relying on some numerical simulations, I show that although adjustments towards the steady-state equilibrium occur through damped oscillations, after an initial period of decline the model predicts a stable union wage premium. |
| Keywords: | Monopoly union model; Capital accumulation; Binding wage contracts; Differential games; Open-loop Stackelberg equilibrium |
| JEL: | J31 J51 J52 |
| Date: | 2024–07–11 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121433 |
| By: | Zi Wang; Xingcheng Xu; Yanqing Yang; Xiaodong Zhu |
| Abstract: | We propose a deep learning framework, DL-opt, designed to efficiently solve for optimal policies in quantifiable general equilibrium trade models. DL-opt integrates (i) a nested fixed point (NFXP) formulation of the optimization problem, (ii) automatic implicit differentiation to enhance gradient descent for solving unilateral optimal policies, and (iii) a best-response dynamics approach for finding Nash equilibria. Utilizing DL-opt, we solve for non-cooperative tariffs and industrial subsidies across 7 economies and 44 sectors, incorporating sectoral external economies of scale. Our quantitative analysis reveals significant sectoral heterogeneity in Nash policies: Nash industrial subsidies increase with scale elasticities, whereas Nash tariffs decrease with trade elasticities. Moreover, we show that global dual competition, involving both tariffs and industrial subsidies, results in lower tariffs and higher welfare outcomes compared to a global tariff war. These findings highlight the importance of considering sectoral heterogeneity and policy combinations in understanding global economic competition. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.17731 |
| By: | Lu Yu |
| Abstract: | For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are not necessarily lattices, we generalize the Abian-Brown and the Markowsky fixed point theorems from single-valued maps to multivalued correspondences. We provide an application in game theory. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.18582 |
| By: | Gabriele Camera (Economic Science Institute, Chapman University); James Gilmore (Economic Science Institute, Chapman University); Marilyn Giselle Hazlett (Economic Science Institute, Chapman University); Jason Shachat (Durham University, Durham University Business School); Bochen Zhu (Wuhan University, Economics and Management School) |
| Abstract: | We study within- and cross-culture interaction in a Stag Hunt game, using a controlled online experiment with Chinese and American participants. We fnd that cross-culture interactions can have a positive impact on efciency. American participants, particularly females, more frequently selected the efcient but risky action when facing a Chinese counterpart. Chinese male participants, instead, less frequently selected the efcient but risky action when facing an American counterpart. These behavioral asymmetries do not support the notion of cultural equivalence, nor the hypothesis that multiculturalism fosters strategic uncertainty. |
| Keywords: | Coordination games, Online experiment, Cultural biases, Gender diferences. |
| JEL: | C92 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:chu:wpaper:24-13 |
| By: | Jose M. Betancourt; Ali Hortaçsu; Aniko Öry; Kevin R. Williams |
| Abstract: | We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with the lowest remaining capacity sells. Because firms do not fully internalize the social option value of future sales, equilibrium prices can be inefficiently low such that both firms and consumers would benefit if firms could commit to higher prices. We term this new welfare effect the Bertrand scarcity trap. |
| JEL: | C7 D04 D6 L0 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32673 |
| By: | Lillethun, Erik; Sharma, Rishi |
| Abstract: | This paper develops a theoretical model of cyberwarfare between nations, focusing on the factors that determine the severity and outcomes of cyber conflicts. We introduce a two-country model where nations invest in offensive or defensive cyber capabilities across networked systems. We show that resource expenditure intensifies when players' effective values are similar, which can help explain the rise of cyberwarfare. We explore the implications of network structures, showing how larger attack surfaces worsen outcomes for defenders. Additionally, we investigate the impact of private cyber defence provision, and find that centralized policies may either improve or exacerbate cyber conflict. |
| Keywords: | cyberwarfare; cyberattacks; networks |
| JEL: | C72 D74 D85 F5 |
| Date: | 2024–06–18 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121299 |
| By: | Park, Hyungmin (University of Warwick); Squintani, Francesco (University of Warwick) |
| Abstract: | We study the choice of multiple advisors, balancing political alignment, competence, and diverse perspectives. An imperfectly informed leader can consult one or two advisors. One has views closely aligned with the leader’s, but his information is imprecise or correlated with the leaders own. The other is more biased but has independent or more precise information. We identify a trade-off between consulting the more aligned or the better informed expert, even when this entails small costs. Subtle comparative statics emerge : When the leader consults both advisors, increasing the bias of the more biased expert may result in the dismissal of the other advisor. The leader may opt to delegate consulting and decision-making, but only to the advisor who collects superior information in equilibrium. We then study the uncertain trade-off case where the most informed advisor is not necessarily also more biased. We find that reducing the probability that the better-informed expert is more biased may lead to hiring also the other advisor. The leader may delegate to the advisor with uncertain bias, although he is more biased in expectation, because he more easily aggregates information in equilibrium. |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1507 |
| By: | Jason R. Blevins |
| Abstract: | Continuous-time formulations of dynamic discrete choice games offer notable computational advantages, particularly in modeling strategic interactions in oligopolistic markets. This paper extends these benefits by addressing computational challenges in order to improve model solution and estimation. We first establish new results on the rates of convergence of the value iteration, policy evaluation, and relative value iteration operators in the model, holding fixed player beliefs. Next, we introduce a new representation of the value function in the model based on uniformization -- a technique used in the analysis of continuous time Markov chains -- which allows us to draw a direct analogy to discrete time models. Furthermore, we show that uniformization also leads to a stable method to compute the matrix exponential, an operator appearing in the model's log likelihood function when only discrete time "snapshot" data are available. We also develop a new algorithm that concurrently computes the matrix exponential and its derivatives with respect to model parameters, enhancing computational efficiency. By leveraging the inherent sparsity of the model's intensity matrix, combined with sparse matrix techniques and precomputed addresses, we show how to significantly speed up computations. These strategies allow researchers to estimate more sophisticated and realistic models of strategic interactions and policy impacts in empirical industrial organization. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.14914 |
| By: | Rosina Rodríguez Olivera |
| Abstract: | I study the incentives of an informed firm to share its private information with its competitor and the incentives of a regulator to constrain or enforce disclosure in order to benefit consumers. Firms offer differentiated goods, compete a là Bertrand and one firm has an information advantage about demand over its competitor. I show that full disclosure of information is optimal for the informed firm, because it increases price correlation and surplus extraction from consumers. A regulator can increase expected consumer surplus and welfare by restricting disclosure, but consumers can benefit from the regulator privately disclosing some information to the competitor. Disclosure increases the ability of firms to extract surplus from consumers, but private disclosure creates a coordination failure in firm pricing. The optimal disclosure policy is chosen to induce goods to be closer substitutes and intensify the competition across firms. |
| Keywords: | Competition, Information |
| JEL: | D18 D43 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_578 |
| By: | Joshua S. Gans |
| Abstract: | When AI prediction substantially resolves trial uncertainty, a party purchasing AI prediction will disclose it if it is in their favour and not otherwise, signalling the outcome to the other party. Thus, the trial outcome becomes common knowledge. However, this implies that the parties will settle rather than purchase the AI prediction. When parties have differing prior beliefs regarding trial outcomes, these differences are only resolved if the AI prediction is purchased and utilised. In this case, AI will be purchased in equilibrium. Different trial cost allocation rules awarding all costs to the losing party (the English Rule) or having each party bear their own costs (the American Rule) can impact the demand for AI for settlement negotiations, but how this occurs interacts with the expectations regarding whether a settlement will occur or not in AI's absence. |
| JEL: | K41 O31 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32685 |
| By: | Robert J. Barro |
| Abstract: | The Hotelling locational model and its adaptations to a circular city provide a core framework for research in industrial organization. The present paper expands the explanatory power of this model by incorporating a continuum of consumers with constant-elasticity demand functions along with stores that have constant marginal costs of production. The stores are evenly spaced in equilibrium. The model generates a simple formula in which the markup of price over marginal cost depends on the spacing between stores and a transportation-cost parameter but is independent of the elasticity of demand. This result reflects pricing decisions by stores that factor in the threat of losing business entirely at the borders with neighboring stores. The free-entry solutions for the number of stores and their spacing approximate socially optimal values but quantities of goods consumed are inefficiently low. |
| JEL: | L1 L12 L13 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32660 |