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on Game Theory |
| By: | Francis Bloch (Universite´ Paris 1 and Paris School of Economics); Bhaskar Dutta (Ashoka University); Marcin Dziubi´nski (Institute of Informatics, University of Warsaw) |
| Abstract: | We propose and study a model of strategic network design and exploration where the hider, subject to a budget constraint restricting the number of links, chooses a connected network and the location of an object. Meanwhile, the seeker, not observing the network and the location of the object, chooses a network exploration strategy starting at a fixed node in the network. The network exploration follows the expanding search paradigm of Alpern and Lidbetter (2013). We obtain a Nash equilibrium and characterize equilibrium payoffs in the case of linking budget allowing for trees only. We also give an upper bound on the expected number of steps needed to find the hider for the case where the linking budget allows for at most one cycle in the network. |
| Keywords: | Network exploration; networks; Strategic hiding |
| Date: | 2024–04–12 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:112&r= |
| By: | Salvador Barberà; Anke Gerber |
| Abstract: | We formalize, under the name of games of addition, the strategic inter- action between agents that can play non-simultaneously by adding payoff relevant actions to those that any other players or themselves have already taken previously, but may also agree unanimously to stop adding them and collect the payoffs associated with the truncated sequence of moves. Our formalization differs from that of extensive form games in that the order of the agents’ moves is not predetermined but emerges endogenously when applying an adapted version of a solution concept proposed by Dutta, Jackson and Le Breton (2004). We provide results regarding the properties of solutions to games of addition, and we also compare their corresponding equilibria with those we would obtain if using extensive form games and subgame perfection as alternative tools of analysis. |
| Keywords: | sequential games, order of play |
| JEL: | C72 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1443&r= |
| By: | Zongxia Liang; Yi Xia; Bin Zou |
| Abstract: | We introduce a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle; the reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus; the competition game between the two reinsurers is settled by a non-cooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semi-closed form. Additionally, we obtain interesting sensitivity results for the equilibrium strategies through both an analytical and numerical study. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.06235&r= |
| By: | Federico Cannerozzi; Giorgio Ferrari |
| Abstract: | We consider ergodic symmetric $N$-player and mean-field games of singular control in both cooperative and competitive settings. The state process dynamics of a representative player follow geometric Brownian motion, controlled additively through a nondecreasing process. Agents aim to maximize a long-time average reward functional with instantaneous profit of power type. The game shows strategic complementarities, in that the marginal profit function is increasing with respect to the dynamic average of the states of the other players, when $N |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.15079&r= |
| By: | Yuya Wakabayashi (JSPS Research Fellow (DC2), Graduate School of Economics, Osaka University) |
| Abstract: | We examine a simple hidden information economy with a single agent, multiple identical firms, and two goods. The agent’s states are unknown to the firms. The game unfolds in two stages: in the first stage, firms offer a menu of allocations, and in the second stage, the agent selects her preferred allocation from the offered allocations. We show that, in almost all cases, the constrained efficient allocation cannot be implemented by a subgame perfect equilibrium in the game. |
| Keywords: | Asymmetric information, Constrained efficiency, Nash implementation |
| JEL: | D47 D82 D86 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:osp:wpaper:24e002&r= |
| By: | Sylvain BARTHÉLÉMY (Gwenlake, Rennes, France); Virginie GAUTIER (TAC Economics and Univ Rennes, CNRS, CREM – UMR6211, F-35000 Rennes France); Fabien RONDEAU (Univ Rennes, CNRS, CREM – UMR6211, F-35000 Rennes France) |
| Abstract: | We study the class of congestion games with player-specic payoff functions Milchtaich (1996). Focusing on a case where the number of resources is equal to two, we give a short and simple method for identifying the exact number of Nash equilibria in pure strategies. We propose an algorithmic method, first to find one or more Nash equilibria; second, to compare the optimal Nash equilibrium, in which the social cost is minimized, with the worst Nash equilibrium, in which the converse is true; third, to identify the time associated to the computations when the number of players increases. |
| Keywords: | currency crises, early warning system, neural network, convolutional neural network, SHAP values. |
| JEL: | F14 F31 F47 |
| Date: | 2024–03 |
| URL: | https://d.repec.org/n?u=RePEc:tut:cremwp:2024-01&r= |
| By: | Shuige Liu |
| Abstract: | We use a uniform framework to cognitive hierarchy (CH) solution concepts a decision-theoretical foundation by the epistemic game theoretical solution concept $\Delta$-rationalizability (Battigalli and Siniscalchi, 2003). We formulate level-$k$ strategic sophistication as an information type, and, by putting intuitive conditions on the the belief of players with a strategic sophistication, we define a restriction $\Delta^\kappa$, from which the levels of reasoning is endogenously determined. We show that in static games, Camerer, Ho, and Chong's (2004) CH solution generically coincides with the behavioral consequence of rationality, common belief in rationality, and transparency of $\Delta^\kappa$; based on this, we connect CH with Bayesian equilibrium. By adapting $\Delta^\kappa$ into dynamic games, we show that Lin and Palfrey's (2024) DCH solution generically coincides with the behavioral consequence of rationality, common strong belief in rationality, and transparency of (dynamic) $\Delta^\kappa$. The same structure could analyze many variations of CH in the literature. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.19623&r= |
| By: | Virginia Cecchini Manara; Eleonora Ciscato; Pietro Guarnieri; Lorenzo Spadoni |
| Abstract: | The urgency of climate, biodiversity, and pollution crises has prompted international and national institutions to move beyond the prevention and mitigation of damages and to design policies aimed at promoting ecological restoration. In this paper, we address this emerging policy challenge by presenting experimental evidence on individuals’ propensity to contribute to restoration activities. Specifically, our design links a common pool resource game to a public good game to investigate how previous resource exploitation influences restoration decisions. We find that history matters since subjects who participate in resource depletion show a different behavior as compared to subjects who are only called to restore it. Specifically, while the former are subject to behavioral lock-ins that influence the success of restoration, the latter are more prompt to restore the more the resource is depleted. |
| Keywords: | Ecological Restoration, Common-pool resource game, Public good game |
| JEL: | C72 C99 Q48 |
| Date: | 2024–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:pie:dsedps:2024/307&r= |
| By: | Christopher P. Chambers; Federico Echenique; Takashi Hayashi |
| Abstract: | This paper studies manipulation of belief aggregation rules in the setting where the society first collects individual's probabilistic opinions and then solves a public portfolio choice problem with common utility based on the aggregate belief. First, we show that belief reporting in Nash equilibrium under the linear opinion pool and log utility is identified as the profile of state-contingent wealth shares in parimutuel equilibrium with risk-neutral preference. Then we characterize belief aggregation rules which are Nash-implementable. We provide a necessary and essentially sufficient condition for implementability, which is independent of the common risk attitude. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.01655&r= |
| By: | Swagata Bhattacharjee (Ashoka University); Srijita Ghosh (Ashoka University); Suraj Shekhar (Ashoka University) |
| Abstract: | We consider a static cheap talk model in an environment with either one or two experts whose biases are privately known by the experts themselves. Before the experts learn the state, they send a cheap talk message about their bias to the decision maker. Subsequently, the decision maker chooses one expert to get state relevant advice from. We ask two questions - One, is there an equilibrium where the experts’ bias is fully revealed? Two, is the bias revealing equilibrium welfare improving for the decision maker? We find that when there is only one expert, there is no bias revealing equilibrium. However, if there are two experts, there exists a bias revealing equilibrium, and under some conditions it gives the decision maker more utility than any equilibrium which is possible without bias revelation. This highlights a new channel through which sender competition can benefit the decision maker, through which sender competition can benefit the decision maker. |
| Keywords: | bias revelation; Cheap talk; multiple senders; uncertain bias |
| Date: | 2024–01–29 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:109&r= |
| By: | Masamitsu Ohnishi; Makoto Shimoshimizu |
| Abstract: | This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties affect the large traders' execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class; it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.07184&r= |
| By: | Xue Cheng; Meng Wang; Ziyi Xu |
| Abstract: | The interactions between a large population of high-frequency traders (HFTs) and a large trader (LT) who executes a certain amount of assets at discrete time points are studied. HFTs are faster in the sense that they trade continuously and predict the transactions of LT. A jump process is applied to model the transition of HFTs' attitudes towards inventories and the equilibrium is solved through the mean field game approach. When the crowd of HFTs is averse to running (ending) inventories, they first take then supply liquidity at each transaction of LT (throughout the whole execution period). Inventory-averse HFTs lower LT's costs if the market temporary impact is relatively large to the permanent one. What's more, the repeated liquidity consuming-supplying behavior of HFTs makes LT's optimal strategy close to uniform trading. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.18200&r= |
| By: | Yifan Zhang |
| Abstract: | Political and advertising campaigns increasingly exploit social networks to spread information and persuade people. This paper studies a persuasion model to examine whether such a strategy is better than simply sending public signals. Receivers in the model have heterogeneous priors and will pass on a signal if they are persuaded by it. I show that a risk neutral or risk loving sender prefers to use public signals, unless more sceptical receivers are sufficiently more connected in the social network. A risk averse sender may prefer to exploit the network. These results still hold when networks exhibit homophily. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.18965&r= |
| By: | Abdoulaye Ndiaye |
| Abstract: | This paper studies the optimal transaction fee mechanisms for blockchains, focusing on the distinction between price-based ($\mathcal{P}$) and quantity-based ($\mathcal{Q}$) controls. By analyzing factors such as demand uncertainty, validator costs, cryptocurrency price fluctuations, price elasticity of demand, and levels of decentralization, we establish criteria that determine the selection of transaction fee mechanisms. We present a model framed around a Nash bargaining game, exploring how blockchain designers and validators negotiate fee structures to balance network welfare with profitability. Our findings suggest that the choice between $\mathcal{P}$ and $\mathcal{Q}$ mechanisms depends critically on the blockchain's specific technical and economic features. The study concludes that no single mechanism suits all contexts and highlights the potential for hybrid approaches that adaptively combine features of both $\mathcal{P}$ and $\mathcal{Q}$ to meet varying demands and market conditions. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.00235&r= |
| By: | Marco Battaglini; Thomas R. Palfrey |
| Abstract: | Collective action is a dynamic process where individuals in a group assess over time the benefits and costs of participating toward the success of a collective goal. Early participation improves the expectation of success and thus stimulates the subsequent participation of other individuals who might otherwise be unwilling to engage. On the other hand, a slow start can depress expectations and lead to failure for the group. Individuals have an incentive to procrastinate, not only in the hope of free riding, but also in order to observe the flow of participation by others, which allows them to better gauge whether their own participation will be useful or simply wasted. How do these phenomena affect the probability of success for a group? As the size of the group increases, will a “power of large numbers” prevail producing successful outcomes, or will a “curse of large numbers” lead to failure? In this paper, we address these questions by studying a dynamic collective action problem in which n individuals can achieve a collective goal if a share of them takes a costly action (e.g., participate in a protest, join a picket line, or sign an environmental agreement). Individuals have privately known participation costs and decide over time if and when to participate. We characterize the equilibria of this game and show that under general conditions the eventual success of collective action is necessarily probabilistic. The process starts for sure, and hence there is always a positive probability of success; however, the process “gets stuck” with positive probability, in the sense that participation stops short of the goal. Equilibrium outcomes have a simple characterization in large populations: welfare converges to either full efficiency or zero as n→∞ depending on a precise condition on the rate at which the share required for success converges to zero. Whether success is achievable or not, delays are always irrelevant: in the limit, success is achieved either instantly or never. |
| JEL: | D71 D74 D82 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32473&r= |
| By: | Sofia Priazhkina; Samuel Palmer; Pablo Martín-Ramiro; Román Orús; Samuel Mugel; Vladimir Skavysh |
| Abstract: | We build a network formation game of firms with trade flows to study the adoption and usage of a new digital currency as an alternative to correspondent banking. We document endogenous heterogeneity and inefficiency in adoption outcomes and explain why higher usage may correspond to lower adoption. Next, we frame the model as a quadratic unconstrained binary optimization (QUBO) problem and apply it to data. Method-wise, QUBO presents an extension to the potential function approach and makes broadly defined network games applicable and empirically feasible, as we demonstrate with a quantum computer. |
| Keywords: | Central bank research; Digital currencies and fintech; Digitalization; Economic models; Financial institutions; Payment clearing and settlement systems; Sectoral balance sheet |
| JEL: | E21 E44 E62 G51 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:24-17&r= |
| By: | Gautam Gowrisankaran; Philipp Schmidt-Dengler |
| Abstract: | This paper analyzes dynamic oligopoly models where investment is the principal strategic variable of interest, there are a large number of investment choices, and there are privately observed shocks to the marginal cost of investment. We show that simulation methods to compute these models can result in non-existence of pure strategy equilibrium. We provide a computationally efficient method to calculate optimal investment probabilities and show how to apply our methods to the recent dynamic empirical literature. The method iteratively finds the investment choices chosen with positive probability and cutoff values of the private information shocks across options in this set. |
| JEL: | C63 C73 L11 L13 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32399&r= |
| By: | Salvador Barberà; Danilo Coelho |
| Abstract: | We propose mechanisms for two parties with potentially conflicting objectives to jointly select a predetermined number of candidates to occupy decision-making positions. Two leading examples of these situations are: i) the selection of an arbitrator panel by two conflicting firms, and ii) the bipartisan coalition's selection of a set of judges to occupy court vacancies. We analyze the efficiency, fairness, and simplicity of equilibrium outcomes in strategic games induced by these mechanisms. Their effectiveness hinges on the parties' preferences over the sets containing the required number of the candidates to be chosen. |
| Keywords: | appointing arbitrators, appointing judges, rule of k name, split appointment rules, compromise, unanimity compromise set, top compromise set |
| JEL: | D02 D71 D72 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1442&r= |
| By: | Adam Hallengreen (Department of Economics, University of Copenhagen); Thomas H. Joergensen (Department of Economics, University of Copenhagen); Annasofie M. Olesen (Department of Economics, University of Copenhagen) |
| Abstract: | In this guide, we introduce the limited commitment model of dynamic household bargaining behavior over the life cycle. The guide is intended to make the limited commitment model more accessible to researchers who are interested in studying intra-household allocations and divorce over the life cycle. We mitigate computational challenges by providing a flexible base of code that can be customized and extended to the specific use case. The main contribution is to discuss practical implementation details of the model class, and provide guidance on how to efficiently solve limited commitment models using state-of-the-art numerical methods. The setup and solution algorithm is presented through a stylized example of dynamic consumption allocation and includes accompanying Python and C++ code used to generate all results. |
| Keywords: | Household Bargaining, limited commitment, life cycle, couples, numerical dynamic programming |
| JEL: | D13 D15 C61 C63 C78 |
| Date: | 2024–05–16 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kucebi:2409&r= |
| By: | Toke S. Aidt; Facundo Albornoz; Esther Hauk |
| Abstract: | This article explores the complex interplay between deforestation policies and foreign influence, using a game theoretical model to analyze geopolitical factors influencing forest conservation decisions in countries with significant rainforests. The model highlights the conflicting interests of foreign powers – one aiming for economic benefits from agriculture and the other advocating for forest preservation due to environmental services. The paper demonstrates how domestic political dynamics and economic shocks influence the regulatory decisions on deforestation. This understanding is crucial for formulating strategies that balance developmental needs and global environmental concerns. |
| Keywords: | foreign influence, geopolitics, deforestation, food security, Brazil, China, rainforest |
| JEL: | D72 D74 O13 Q23 P33 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1441&r= |