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on Game Theory |
| By: | Mouli Modak (Chapman University) |
| Abstract: | In this experimental paper, the author investigates the framing effect of different representations of multiple strategic settings or games on a player’s strategic behavior. Two representations of the same environment are employed, wherein a player engages in two infinitely repeated prisoner’s dilemma games. In the first representation (termed Split), the stage games are shown separately. In contrast, the second representation (termed Linked) displays a combined stage game. The choice bracketing, distinguishing between Narrow and Broad bracketing, is considered a potential cause behind any disparity in behavior between the two representations. The Split representation does not necessitate broad bracketing, whereas the Linked representation compels it. Each type of bracketing has its own equilibrium implications. The author employs both a between-subject design (Study 1), where each subject observes only one representation, and a within-subject design (Study 2), where each subject is shown both the Linked and Split representations. In Study 1, significant differences in average behavior between the two representations are observed for both symmetric and asymmetric payoffs, albeit only after conditioning for session fixed effects. Study 2 reveals a more prominent effect of representation, and a sequence effect is observed, wherein the tendency to defect in both games is higher in the Linked representation if administered after the Split representation. In Study 2, for individuals who cannot be categorized as broad bracketers, the effect of seeing the Linked representation instead of the Split representation is economically significant. It increases the probability of choosing to cooperate in both games by more than 20% and decreases the probability to defect in both games by more than 25%. |
| Keywords: | Framing efect, Choice bracketing, Infnitely Repeated Prisoner’s Dilemma Game, Asymmetry, Between-subject, Within-subject |
| JEL: | C72 C91 D91 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:24-03&r=gth |
| By: | Yohan Pelosse (Humanities and Social Sciences, Swansea University) |
| Abstract: | In the literature on conflicts, the rule that determines the ’win probabilities’ of the contestants is often specified by a mapping –contest success function (CSF)—which translates the effort vectors into a set of win probabilities. When these mappings correspond to the choice probabilities of the Luce model (Luce (1959)), this gives rise to the popular Luce-contest success function (CSF). The use of this specific model in conflicts remains unclear: How does the Luce CSF rule get generated in the first place and what are the choice probabilities actually representing in a conflict ? Are they individual probabilities of winning the prize, or a share of the resources allocated to each contestant ? This paper shows that the Luce CSF can take on these two interpretations simultaneously within a single non-cooperative environment. We carry out this exercise by following and extending the strategic approach of the Shapley value initiated by Ui (2000). Our main methodological innovation is to connect the class of TU games with action choices of a strategic game to its ’aggregate deviation functions’. Considering a class of anti-coordination games, we then obtain two main results. Our firstmain theoremstates that the ’Luce values’ –which represent the ’impact functions’ in the case of a contest– are given by the Shapley value of the TU games with action choices associated to the non-cooperative game when the players’ belief are in equilibrium. Our second ’representation theorem’ relates the axioms given by Skaperdas (1996) to represent the logit CSF as the solution of the TU-games associated to the non-cooperative game when the players’ belief are in equilibrium and the axioms of Shapley hold for this solution. In this case, our approach singles out the specific class of Luce CSFs of the Tullock and power-forms as the only possible forms of CSFs. Hence, in this sense, our results show that the Luce CSFs can be given a ’non-cooperative Shapley’ representation. As a corollary, we discuss how our approachmay also provide a non-cooperative theory to the quasivalue order representation of stochastic rules introduced inMonderer and Gilboa (1992). |
| JEL: | C72 C92 D83 |
| Date: | 2024–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:swn:wpaper:2024-01&r=gth |
| By: | Banerjee, Sreoshi |
| Abstract: | We model sequencing problems as coalitional games and study the Shapley value and the non-emptiness of the core. The ”optimistic” cost of a coalition is its minimum waiting cost when the members are served first in an order. The ”pessimistic” cost of a coalition is its minimum waiting cost when the members are served last. We take the weighted average of the two extremes and define the class of ”weighted optimistic pessimistic (WOP)” cost games. If the weight is zero, we get the optimistic scenario and if it is one, we get the pessimistic scenario. We find a necessary and sufficient condition on the associated weights for the core to be non-empty. We also find a necessary and sufficient condition on these weights for the Shapley value to be an allocation in the core. We impose ”upper bounds” to protect agents against arbitrarily high disuilities from waiting. If an agent’s disutility level is his Shapley payoff from the WOP cost game, we find necessary and sufficient conditions on the upper bounds for the Shapley value to conform to them. |
| Keywords: | Sequencing, disutility upper bounds, core, cooperative game, Shapley value |
| JEL: | C71 C72 D61 D63 |
| Date: | 2024–02–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120188&r=gth |
| By: | Guy Aridor; Rava Azeredo da Silveira; Michael Woodford |
| Abstract: | We analyze a coordination game with information-constrained players. The players’ actions are based on a noisy compressed representation of the game’s payoffs in a particular case, where the compressed representation is a latent state learned by a variational autoencoder (VAE). Our generalized VAE is optimized to trade off the average payoff obtained over a distribution of possible games against a measure of the congruence between the agent’s internal model and the statistics of its environment. We apply our model to the coordination game in the experiment of Frydman and Nunnari (2023), and show that it offers an explanation for two salient features of the experimental evidence: both the relatively continuous variation in the players’ action probabilities with changes in the game payoffs, and the dependence of the degree of stochasticity of players’ choices on the range of game payoffs encountered on different trials. Our approach also provides an account of the way in which play should gradually adjust to a change in the distribution of game payoffs that are encountered, offering an explanation for the history-dependent play documented by Arifovic et al. (2013). |
| Keywords: | global games, experiments, autoencoder, cognitive noise |
| JEL: | C45 C63 C73 C92 D91 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10935&r=gth |
| By: | Francesc Dilmé |
| Abstract: | This paper introduces and analyzes sequentially stable outcomes in extensive-form games. An outcome ω is sequentially stable if, for any ǫ >0 and any small enough perturbation of the players’ behavior, there is an ǫ-perturbation of the players’ payoffs and a corresponding equilibrium with outcome close to ω. Sequentially stable outcomes exist for all finite games and are outcomes of sequential equilibria. They are closely related to stable sets of equilibria and satisfy versions of forward induction, iterated strict equilibrium dominance, and invariance to simultaneous moves. In signaling games, sequentially stable outcomes pass the standard selection criteria, and when payoffs are generic, they coincide with outcomes of stable sets of equilibria. |
| Keywords: | Sequentially stability, stable outcome, signaling games |
| JEL: | C72 C73 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_511&r=gth |
| By: | Daniele De Luca |
| Abstract: | This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to cooperate. We can then define actual and potential power as special relations between different states of the system. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2401.16406&r=gth |
| By: | Robert Denkert; Ulrich Horst |
| Abstract: | We establish a probabilistic framework for analysing extended mean-field games with multi-dimensional singular controls and state-dependent jump dynamics and costs. Two key challenges arise when analysing such games: the state dynamics may not depend continuously on the control and the reward function may not be u.s.c.~Both problems can be overcome by restricting the set of admissible singular controls to controls that can be approximated by continuous ones. We prove that the corresponding set of admissible weak controls is given by the weak solutions to a Marcus-type SDE and provide an explicit characterisation of the reward function. The reward function will in general only be u.s.c.~To address the lack of continuity we introduce a novel class of MFGs with a broader set of admissible controls, called MFGs of parametrisations. Parametrisations are laws of state/control processes that continuously interpolate jumps. We prove that the reward functional is continuous on the set of parametrisations, establish the existence of equilibria in MFGs of parametrisations, and show that the set of Nash equilibria in MFGs of parametrisations and in the underlying MFG with singular controls coincide. This shows that MFGs of parametrisations provide a canonical framework for analysing MFGs with singular controls and non-linear jump impact. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.09317&r=gth |
| By: | David Lowing; Léa Munich; Kevin Techer |
| Abstract: | Accurate cost allocation is a challenge for both public service operators and regulatory bodies, given the dual objectives of ensuring essential public service provision and maintaining fair competition. Operators have the obligation to provide essential public services for all individuals, which may incur additional costs. To compensate this, the operators receive state aids, which are determined by an assessment of the net cost associated with these obligations. However, these aids introduce the risk of distorting competition, as operators may employ them to subsidize competitive activities. To avoid this risk, a precise cost allocation method that adequately assess the net cost of these obligations becomes necessary. Such a method must satisfy specific properties that effectively prevent cross-subsidization. In this paper, we propose a method grounded in cooperative game theory that offers a solution for allocating common costs between activities and obligations in public service provision. We adopt a normative approach by introducing a set of desirable axioms that prevent cross-subsidization. We provide two characterizations of our proposed solution on the basis of these axioms. Furthermore, we present an illustration of our method to the allocation of common costs for a public service operator. |
| Keywords: | Cooperative game theory; Cost allocation; Public service; Cross-subsidization. |
| JEL: | C71 L51 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2024-03&r=gth |
| By: | Scott Duke Kominers; Jesse M. Shapiro |
| Abstract: | A sender sends a signal about a state to a receiver who takes an action that determines a payoff. A moderator can block some or all of the sender's signal before it reaches the receiver. When the moderator's policy is transparent to the receiver, the moderator can improve the payoff by blocking false or harmful signals. When the moderator's policy is opaque, however, the receiver may not trust the moderator. In that case, the moderator can guarantee an improved outcome only by blocking signals that enable harmful acts. Blocking signals that encourage false beliefs can be counterproductive. |
| JEL: | D47 D82 D83 L82 L86 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32156&r=gth |
| By: | Alireza Fallah; Michael I. Jordan; Ali Makhdoumi; Azarakhsh Malekian |
| Abstract: | We study a three-layer data market comprising users (data owners), platforms, and a data buyer. Each user benefits from platform services in exchange for data, incurring privacy loss when their data, albeit noisily, is shared with the buyer. The user chooses platforms to share data with, while platforms decide on data noise levels and pricing before selling to the buyer. The buyer selects platforms to purchase data from. We model these interactions via a multi-stage game, focusing on the subgame Nash equilibrium. We find that when the buyer places a high value on user data (and platforms can command high prices), all platforms offer services to the user who joins and shares data with every platform. Conversely, when the buyer's valuation of user data is low, only large platforms with low service costs can afford to serve users. In this scenario, users exclusively join and share data with these low-cost platforms. Interestingly, increased competition benefits the buyer, not the user: as the number of platforms increases, the user utility does not improve while the buyer utility improves. However, increasing the competition improves the overall utilitarian welfare. Building on our analysis, we then study regulations to improve the user utility. We discover that banning data sharing maximizes user utility only when all platforms are low-cost. In mixed markets of high- and low-cost platforms, users prefer a minimum noise mandate over a sharing ban. Imposing this mandate on high-cost platforms and banning data sharing for low-cost ones further enhances user utility. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.09697&r=gth |
| By: | Mingyang Li; Han Pengsihua; Songqing Zhao; Zejun Wang; Limin Yang; Weian Liu |
| Abstract: | On August 24, 2023, Japan controversially decided to discharge nuclear wastewater from the Fukushima Daiichi Nuclear Power Plant into the ocean, sparking intense domestic and global debates. This study uses evolutionary game theory to analyze the strategic dynamics between Japan, other countries, and the Japan Fisheries Association. By incorporating economic, legal, international aid, and environmental factors, the research identifies three evolutionarily stable strategies, analyzing them via numerical simulations. The focus is on Japan's shift from wastewater release to its cessation, exploring the myriad factors influencing this transition and their effects on stakeholders' decisions. Key insights highlight the need for international cooperation, rigorous scientific research, public education, and effective wastewater treatment methods. Offering both a fresh theoretical perspective and practical guidance, this study aims to foster global consensus on nuclear wastewater management, crucial for marine conservation and sustainable development. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.07210&r=gth |
| By: | Fakhrabadi, Mahnaz (Dept. of Business and Management Science, Norwegian School of Economics); Sandal, Leif K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | This study delves into a dynamic Stackelberg game comprised of a manufacturer and a retailer, operating in an environment with fluctuating demand and price-dependent consumer behavior. The multi-period optimization challenges the manufacturer to strategically set wholesale and buyback prices, while the retailer determines the retail price and order quantities within a single contract. In this dynamic framework, the players operate under the constraints of a cap-and-trade policy, with limited knowledge of demand distributions, characterized only by mean and standard deviation parameters. To address this inherent uncertainty, we employ a distributionally robust approach. Additionally, we explore the enduring effects of historical decisions on present-day demand, reflecting a memory-like market behavior. Through numerical examples, we illuminate the influence of buyback contracts and cap-and-trade policies on decision-making processes within this setting. |
| Keywords: | Cap-and-Trade Policy; Multi-Period Stackelberg Game; Distributional-Robust Demand; Single Contract; Buyback Contract; Sustainability |
| JEL: | C61 C62 C63 C72 C73 D81 Q52 |
| Date: | 2024–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2024_005&r=gth |
| By: | Zdybel, Karol B. |
| Abstract: | Spontaneous norms, or simply norms, can be defined as rules of conduct that emerge without intentional design and in the absence of purposeful external coordination. While the law and economics scholarship has formally analyzed spontaneous norms, the analysis has typically been limited to scenarios where agents possess complete information about the interaction structure, including others' understanding of desirable and undesirable outcomes. In contrast, this paper examines spontaneous norms under the assumption of agent heterogeneity and private preferences. By employing a game-theoretical framework, the analysis reveals that norms' lifecycle can be divided into a formative phase and a long-run phase. The formative phase crucially shapes the norm's content and is itself critically dependent on the initial beliefs that agents hold about each other. Moreover, spontaneous norms are resilient to minor shocks to the belief structure but disintegrate when the magnitude of shocks becomes significant. In the final part, the paper highlights the broader implications of its findings, indicating applications in general law and economics, legal anthropology and history, and the sociology of social norms. |
| Keywords: | Spontaneous norms, Social norms, Custom, Private assessment, Legal history |
| JEL: | K00 K10 K39 P48 Z13 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ilewps:78&r=gth |
| By: | Simina Br\^anzei; MohammadTaghi Hajiaghayi; Reed Phillips; Suho Shin; Kun Wang |
| Abstract: | We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at a point of her choice, while Bob chooses the left piece or the right piece, leaving the remainder for Alice. We consider two versions: sequential, where Bob observes Alice's cut point before choosing left/right, and simultaneous, where he only observes her cut point after making his choice. The simultaneous version was first considered by Aumann and Maschler (1995). We observe that if Bob is almost myopic and chooses his favorite piece too often, then he can be systematically exploited by Alice through a strategy akin to a binary search. This strategy allows Alice to approximate Bob's preferences with increasing precision, thereby securing a disproportionate share of the resource over time. We analyze the limits of how much a player can exploit the other one and show that fair utility profiles are in fact achievable. Specifically, the players can enforce the equitable utility profile of $(1/2, 1/2)$ in the limit on every trajectory of play, by keeping the other player's utility to approximately $1/2$ on average while guaranteeing they themselves get at least approximately $1/2$ on average. We show this theorem using a connection with Blackwell approachability. Finally, we analyze a natural dynamic known as fictitious play, where players best respond to the empirical distribution of the other player. We show that fictitious play converges to the equitable utility profile of $(1/2, 1/2)$ at a rate of $O(1/\sqrt{T})$. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.08547&r=gth |
| By: | Tao Lin; Yiling Chen |
| Abstract: | We study a repeated Bayesian persuasion problem (and more generally, any generalized principal-agent problem with complete information) where the principal does not have commitment power and the agent uses algorithms to learn to respond to the principal's signals. We reduce this problem to a one-shot generalized principal-agent problem with an approximately-best-responding agent. This reduction allows us to show that: if the agent uses contextual no-regret learning algorithms, then the principal can guarantee a utility that is arbitrarily close to the principal's optimal utility in the classic non-learning model with commitment; if the agent uses contextual no-swap-regret learning algorithms, then the principal cannot obtain any utility significantly more than the optimal utility in the non-learning model with commitment. The difference between the principal's obtainable utility in the learning model and the non-learning model is bounded by the agent's regret (swap-regret). If the agent uses mean-based learning algorithms (which can be no-regret but not no-swap-regret), then the principal can do significantly better than the non-learning model. These conclusions hold not only for Bayesian persuasion, but also for any generalized principal-agent problem with complete information, including Stackelberg games and contract design. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.09721&r=gth |
| By: | Burani, Nadia; Mantovani, Andrea |
| Abstract: | We consider a duopolistic market in which a green firm competes with a brown rival, and both firms offer vertically differentiated products. Consumers are heterogeneous in both their willingness to pay for intrinsic quality and environmental concern. The latter is positively related to the green firm's market share, giving rise to a green network e¤ect. We characterize how price and quality schedules are set and how consumers sort between the two firms at the market equilibrium. When considering pollution both from consumption and production, we compute total welfare and evaluate the impact of an emission tax and a subsidy for the consumption of the green good. Our analysis demonstrates that efficiency can be achieved through an emission tax, which restores the optimal differential between firms' intrinsic qualities, combined with a discriminatory subsidy, which restores the optimal sorting of consumers. |
| Keywords: | bidimensional product differentiation; environmental concern; green network effect; pollution emissions; price discrimination; subsidy |
| JEL: | D21 L13 H21 Q58 Q51 |
| Date: | 2024–02–26 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:129135&r=gth |
| By: | Kai Hao Yang (Yale University); Philipp Strack (Yale University) |
| Abstract: | A signal is privacy-preserving with respect to a collection of privacy sets, if the posterior probability assigned to every privacy set remains unchanged conditional on any signal realization. We characterize the privacy-preserving signals for arbitrary state space and arbitrary privacy sets. A signal is privacy-preserving if and only if it is a garbling of a reordered quantile signal. These signals are equivalent to couplings, which in turn lead to a characterization of optimal privacy-preserving signals for a decision-maker. We demonstrate the applications of this characterization in the contexts of algorithmic fairness, price discrimination, and information design. |
| Date: | 2023–07–03 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2379&r=gth |