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on Game Theory |
| By: | Nizar Allouch; Luis A.Guardiola; A. Meca |
| Abstract: | Measuring individual productivity (or equivalently distributing the overall productivity) in a network structure of workers displaying peer effects has been a subject of ongoing interest in many areas ranging from academia to industry. In this paper, we propose a novel approach based on cooperative game theory that takes into account the peer effects of worker productivity represented by a complete bipartite network of in- teractions. More specifically, we construct a series of cooperative games where the characteristic function of each coalition of workers is equal to the sum of each worker intrinsic productivity as well as the productivity of other workers within a distance discounted by an attenuation factor. We show that these (truncated) games are balanced and converge to a balanced game when the distance of influence grows large. We then provide an explicit formula for the Shapley value and propose an alternative coalitionally stable distribution of productivity which is computationally much more tractable than the Shapley value. Lastly, we characterize this alternative distribution based on three sensible properties of a logistic network. This analysis enhances our understanding of game-theoretic analysis within logistics networks, offering valuable insights into the peer effects’ impact when assessing the overall productivity and its distribution among workers. |
| Keywords: | Productivity; peer effects; complete bipartite networks; cooperative games |
| URL: | http://d.repec.org/n?u=RePEc:ukc:ukcedp:2302&r=gth |
| By: | Niko Jaakkola; Florian Wagener; Florian O.O. Wagener |
| Abstract: | We define a differential game of public investment with a discontinuous Markovian strategy space. The best response correspondence for the game is well-behaved: a best response exists and uniquely maps almost all profiles of opponents’ strategies back to the strategy space. Our chosen strategy space thus makes the differential game well-formed as a static game in Markovian strategies, resolving a long-standing open problem in the literature. We provide a user-friendly necessary and sufficient condition for constructing the best response. Our methods do not require specific functional forms. Our theory has general applications, including to problems of noncooperative control of stock pollutants, harvesting of natural resources, and joint investment problems. |
| Keywords: | differential games, Markov-perfect Nash equilibria, dynamic public investment |
| JEL: | C72 C73 H41 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10585&r=gth |
| By: | Evan Friedman; Duarte Gon\c{c}alves |
| Abstract: | Quantal response equilibrium (QRE), a statistical generalization of Nash equilibrium, is a standard benchmark in the analysis of experimental data. Despite its influence, nonparametric characterizations and tests of QRE are unavailable beyond the case of finite games. We address this gap by completely characterizing the set of QRE in a class of binary-action games with a continuum of types. Our characterization provides sharp predictions in settings such as global games, the volunteer's dilemma, and the compromise game. Further, we leverage our results to develop nonparametric tests of QRE. As an empirical application, we revisit the experimental data from Carrillo and Palfrey (2009) on the compromise game. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.08011&r=gth |
| By: | Laura Doval; Ran Eilat |
| Abstract: | An analyst observes the frequency with which an agent takes actions, but not the frequency with which she takes actions conditional on a payoff relevant state. In this setting, we ask when the analyst can rationalize the agent's choices as the outcome of the agent learning something about the state before taking action. Our characterization marries the obedience approach in information design (Bergemann and Morris, 2016) and the belief approach in Bayesian persuasion (Kamenica and Gentzkow, 2011) relying on a theorem by Strassen (1965) and Hall's marriage theorem. We apply our results to ring-network games and to identify conditions under which a data set is consistent with a public information structure in first-order Bayesian persuasion games. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.13849&r=gth |
| By: | Shiheng Wang |
| Abstract: | Counterfactual Regret Minimization(CFR) has shown its success in Texas Hold'em poker. We apply this algorithm to another popular incomplete information game, Mahjong. Compared to the poker game, Mahjong is much more complex with many variants. We study two-player Mahjong by conducting game theoretical analysis and making a hierarchical abstraction to CFR based on winning policies. This framework can be generalized to other imperfect information games. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.12087&r=gth |
| By: | Ludovic Tangpi; Shichun Wang |
| Abstract: | In this paper we further extend the optimal bubble riding model proposed by Tangpi and Wang by allowing for price-dependent entry times. Agents are characterized by their individual entry threshold that represents their belief in the strength of the bubble. Conversely, the growth dynamics of the bubble is fueled by the influx of players. Price-dependent entry naturally leads to a mean field game of controls with common noise and random entry time, for which we provide an existence result. The equilibrium is obtained by first solving discretized versions of the game in the weak formulation and then examining the measurability property in the limit. In this paper, the common noise comes from two sources: the price of the asset which all agents trade, and also the exogenous bubble burst time, which we also discretize and incorporate into the model via progressive enlargement of filtration. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.11340&r=gth |
| By: | Bryan S. Graham; Andrin Pelican |
| Abstract: | This paper introduces a simulation algorithm for evaluating the log-likelihood function of a large supermodular binary-action game. Covered examples include (certain types of) peer effect, technology adoption, strategic network formation, and multi-market entry games. More generally, the algorithm facilitates simulated maximum likelihood (SML) estimation of games with large numbers of players, $T$, and/or many binary actions per player, $M$ (e.g., games with tens of thousands of strategic actions, $TM=O(10^4)$). In such cases the likelihood of the observed pure strategy combination is typically (i) very small and (ii) a $TM$-fold integral who region of integration has a complicated geometry. Direct numerical integration, as well as accept-reject Monte Carlo integration, are computationally impractical in such settings. In contrast, we introduce a novel importance sampling algorithm which allows for accurate likelihood simulation with modest numbers of simulation draws. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.11857&r=gth |
| By: | Ananya Parashar; Ludovic Tangpi |
| Abstract: | In this paper, we study the portfolio optimization problem formulated by Lacker and Soret. They formulate a finite time horizon model that allows agents to be competitive, measuring their utility not only by their absolute wealth but also relative performance compared to the average of other agents. While the finite population or $n$-player game is tractable in some cases, the authors present the Mean Field Game framework to solve this problem. Here, we seek to use this framework to clearly detail the optimal investment and consumption strategies in the CRRA utility case as was briefly outlined in Lacker and Soret, but also derive a solution in the CARA utility case. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.10540&r=gth |
| By: | Roweno J. R. K. Heijmans |
| Abstract: | This paper studies policy design in coordination problems. In coordination games, a subsidy raises player $i$'s incentive to play the subsidized action. This raises $j$'s incentive to play the same action, which further incentivizes $i$, and so on. Building upon this ``unraveling effect'', we characterize the subsidies that implement a given outcome of the game as its unique equilibrium. Among other properties, we establish that subsidies are: (i) symmetric for identical players; (ii) globally continuous in model parameters; (iii) increasing in opportunity costs; and (iv) decreasing in spillovers. Applications of the model include joint investment problems, participation decisions, and principal-agent contracting. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.08557&r=gth |
| By: | Daniele De Luca |
| Abstract: | The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product function onto the individual utility function, where the weights can be represented through directed graphs that reflect a situation of power among the players. It is then possible to define some global indices of the system, such as the level of hierarchy, mutualism and freedom, and measure their effects on game equilibria. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.14170&r=gth |
| By: | Nicholas Wu |
| Abstract: | I consider a model of strategic experimentation where agents partake in risky research with payoff externalities; a breakthrough grants the discoverer (winner) a different payoff than the non-discoverers (losers). I characterize the first-best solution and show that the noncooperative game is generically inefficient. Simple contracts sharing payoffs between winner and losers restore efficiency, even when actions are unobserved. Alternatively, if the winner's identity is not contractible, contracting on effort only at the time of breakthrough also restores efficiency. These results suggest that although strategic experimentation generically entails inefficiency, sharing credit is a robust and effective remedy. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.12104&r=gth |
| By: | Bryce Morsky; Fuwei Zhuang; Zuojun Zhou |
| Abstract: | We study the roles of social and individual learning on outcomes of the Minority Game model of a financial market. Social learning occurs via agents adopting the strategies of their neighbours within a social network, while individual learning results in agents changing their strategies without input from other agents. In particular, we show how social learning can undermine efficiency of the market due to negative frequency dependent selection and loss of strategy diversity. The latter of which can lock the population into a maximally inefficient state. We show how individual learning can rescue a population engaged in social learning from such inefficiencies. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.11846&r=gth |
| By: | Itai Arieli; Yakov Babichenko; Fedor Sandomirskiy |
| Abstract: | We consider a model of Bayesian persuasion with one informed sender and several uninformed receivers. The sender can affect receivers' beliefs via private signals, and the sender's objective depends on the combination of induced beliefs. We reduce the persuasion problem to the Monge-Kantorovich problem of optimal transportation. Using insights from optimal transportation theory, we identify several classes of multi-receiver problems that admit explicit solutions, get general structural results, derive a dual representation for the value, and generalize the celebrated concavification formula for the value to multi-receiver problems. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.07672&r=gth |
| By: | Panagiotis Kyriazis; Edmund Lou |
| Abstract: | Coordination facilitation and efficient decision-making are two essential components of successful leadership. In this paper, we take an informational approach and investigate how followers' information impacts coordination and efficient leadership in a model featuring a leader and a team of followers. We show that efficiency is achieved as the unique rationalizable outcome of the game when followers possess sufficiently imprecise information. In contrast, if followers have accurate information, the leader may fail to coordinate them toward the desired outcome or even take an inefficient action herself. We discuss the implications of the results for the role of leaders in the context of financial fragility and crises. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.13841&r=gth |
| By: | José L. Moraga-González; Makoto Watanabe; José Luis Moraga Gonzalez |
| Abstract: | This paper studies how selling constraints, which refer to the inability of firms to attend to all the buyers who want to inspect their products, affect the equilibrium price and social welfare. We show that the price that maximizes social welfare is greater than the marginal cost. This is because with selling constraints, a higher price, despite reducing the probability of trade (fewer buyers are willing to pay a higher price) increases the value of trade (only trades generating positive surplus are consummated). We show that the equilibrium price is inefficiently high except in the limit when firms’ selling constraints vanish and consumers observe prices before they visit firms. Thus, selling constraints constitute a source of market power. |
| Keywords: | price competition, market power, capacity- and selling-constrained firms |
| JEL: | D40 J60 L10 L80 R30 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10583&r=gth |
| By: | Ming Chen; Sareh Nabi; Marciano Siniscalchi |
| Abstract: | This paper proposes a learning model of online ad auctions that allows for the following four key realistic characteristics of contemporary online auctions: (1) ad slots can have different values and click-through rates depending on users' search queries, (2) the number and identity of competing advertisers are unobserved and change with each auction, (3) advertisers only receive partial, aggregated feedback, and (4) payment rules are only partially specified. We model advertisers as agents governed by an adversarial bandit algorithm, independent of auction mechanism intricacies. Our objective is to simulate the behavior of advertisers for counterfactual analysis, prediction, and inference purposes. Our findings reveal that, in such richer environments, "soft floors" can enhance key performance metrics even when bidders are drawn from the same population. We further demonstrate how to infer advertiser value distributions from observed bids, thereby affirming the practical efficacy of our approach even in a more realistic auction setting. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.11732&r=gth |