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on Game Theory |
| By: | Richard P. McLean (Rutgers University); Andrew Postlewaite (University of Pennsylvania) |
| Abstract: | Standard mechanism design begins with a statement of the problem, including knowledge on the designer's part about the distribution of the characteristics (preferences and information) of the participants who are to engage with the mechanism. There is a large literature on robust mechanism design, much of which aims to reduce the assumed information the designer has about the participants. In this paper we provide an auction mechanism that reduces the assumed information assumed of the seller, and, in addition, relaxes substantially the assumed information of the participants. In particular, the mechanism performs well when there are many buyers, even though there is no prior distribution over the accuracy of buyers' information on the part of the designer or the participants. |
| Keywords: | Robustness, Optimal auctions, Incentive Compatibility, Mechanism Design, Interdependent Values, Informational Size, Common Knowledge |
| JEL: | C70 D44 D60 D82 |
| Date: | 2024–10–31 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:24-035 |
| By: | Erhan Bayraktar; Nikolaos Kolliopoulos |
| Abstract: | We consider an $N$-player game where the players control the drifts of their diffusive states which have no interaction in the noise terms. The aim of each player is to minimize the expected value of her cost, which is a function of the player's state and the empirical measure of the states of all the players. Our aim is to determine the $N \to \infty$ asymptotic behavior of the upper order statistics of the player's states under Nash equilibrium (the Nash states). For this purpose, we consider also a system of interacting diffusions which is constructed by using the Master PDE of the game and approximates the system of the Nash states, and we improve an $L^2$ estimate for the distance between the drifts of the two systems which has been used for establishing Central Limit Theorems and Large Deviations Principles for the Nash states in the past. By differentiating the Master PDE, we obtain that estimate also in $L^{\infty}$, which allows us to control the Radon-Nikodym derivative of a Girsanov transformation that connects the two systems. The latter allows us to reduce the problem to the case of $N$ uncontrolled diffusions with standard mean-field interaction in the drifts, which has been treated in a previous work. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18869 |
| By: | Stefano Vannucci |
| Abstract: | Categories of coalitional, strategic and extensive game forms are defined and shown to be isomorphic to full subcategories of the category Chu(Set, 2) of Chu spaces. Categories of coalitional, strategic and extensive games that amount to categoriesof multi-preordered-typed Chu spaces are also introduced and discussed. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:usi:wpaper:918 |
| By: | Emir Kamenica; Xiao Lin |
| Abstract: | When does a Sender, in a Sender-Receiver game, strictly value commitment? In a setting with finite actions and finite states, we establish that, generically, Sender values commitment if and only if he values randomization. In other words, commitment has no value if and only if a partitional experiment is optimal under commitment. Moreover, if Sender's preferred cheap-talk equilibrium necessarily involves randomization, then Sender values commitment. We also ask: how often (i.e., for what share of preference profiles) does commitment have no value? For any prior, any independent, atomless distribution of preferences, and any state space: if there are $\left|A\right|$ actions, the likelihood that commitment has no value is at least $\frac{1}{\left|A\right|^{\left|A\right|}}$. As the number of states grows large, this likelihood converges precisely to $\frac{1}{\left|A\right|^{\left|A\right| }}$. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17503 |
| By: | Michalis Drouvelis; Nobuyuki Hanaki; Yuta Shimodaira |
| Abstract: | Extending the power-to-take game, we explore the impact of two forces that may shape retaliation. In our 2x2 design, i) in addition to taking, the proposers can give part of their endowment to the responders, and ii) in addition to destroying their own endowment in retaliation, the responders can destroy the proposer’s endowment. Although these added options lead the responders to retaliate more severely, they do not significantly influence the proposers’ behavior. It is only when the proposers can give, and the responders can concurrently destroy the endowment of the proposers that the proposers take significantly less from the responders. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1262 |
| By: | Dehez, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium); Mêgnigbêto, Eustache (University of Antwerp) |
| Abstract: | We generalize the 3-player game introduced by Mêgnigbêto (2018) to analyze the synergies existing between universities, the industry and the government in the Triple Helix, a model of research and innovation introduced by Leydesdorff and Etzkowitz (1995). We consider situations involving any number of actors and we allow for a differentiation of their contributions. The resulting game has nonnegative Harsanyi dividends, implying its convexity. The relative size of the core measures the extent of the synergies and the Shapley value measures the contribution of each actor to these synergies. |
| Date: | 2024–04–01 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2024006 |
| By: | Martimort, David; Stole, Lars |
| Abstract: | We study menu auction games in which several principals influence the choice of a privately-informed agent by simultaneously offering action-contingent payments; the agent is free to accept any subset of the offers. Building on tools from non-smooth optimal control with type-dependent participation constraints, we provide necessary conditions for any equilibrium allocation as the (constrained) maximizer of an endogenous aggregate virtual-surplus program. The aggregate maximand includes an information-rent component which captures how the principals’ rent-extraction motives combine. Although there is a large set of equilibria, including equilibrium allocations with discontinuities, we isolate one particular equilibrium allocation, the maximal allocation, which is the solution to an unconstrained maximization program. Under weak conditions, necessary conditions for a maximal allocation are also sufficient, and the corresponding equilibrium tariff offers are easily constructed. We illustrate our findings and derive some economic implications in several applications, with principals having either congruent interests (e.g., public goods collective action games), opposed interests (e.g., pork barrel politics, lobbying), and protection for sale in an international trade context. |
| Keywords: | Menu auctions;; delegated common agency;; screening contracts;; non-smooth optimization problems;; public goods games; ; collective action;; pork barrel politics; ; positive theory of regulation;; protection for sale |
| Date: | 2024–11–14 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:129924 |
| By: | Yann Bouteiller; Karthik Soma; Giovanni Beltrame |
| Abstract: | The universe involves many independent co-learning agents as an ever-evolving part of our observed environment. Yet, in practice, Multi-Agent Reinforcement Learning (MARL) applications are usually constrained to small, homogeneous populations and remain computationally intensive. In this paper, we study how large heterogeneous populations of learning agents evolve in normal-form games. We show how, under assumptions commonly made in the multi-armed bandit literature, Multi-Agent Policy Gradient closely resembles the Replicator Dynamic, and we further derive a fast, parallelizable implementation of Opponent-Learning Awareness tailored for evolutionary simulations. This enables us to simulate the evolution of very large populations made of heterogeneous co-learning agents, under both naive and advanced learning strategies. We demonstrate our approach in simulations of 200, 000 agents, evolving in the classic games of Hawk-Dove, Stag-Hunt, and Rock-Paper-Scissors. Each game highlights distinct ways in which Opponent-Learning Awareness affects evolution. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17466 |
| By: | Armando Holzknecht; Jürgen Huber; Michael Kirchler; Tibor Neugebauer |
| Abstract: | In a pre-registered laboratory asset market study, we investigate dynamics of asset markets with zero (or close to zero) fundamental values. We introduce the “greater fool asset market game” with a zero-value token, whose price doubles in each period. We design several treatments, which differ in terms of whether the fundamental value is zero for sure, and whether the rather low probability of non-zero fundamentals is known (Risk) or not (Ambiguity). We find that prices in markets with zero fundamental value are clearly above zero. Furthermore, we report that prices in treatment Ambiguity are substantially higher than those in the baseline and in treatment Risk. Finally, we show that beliefs regarding the asset’s value and others’ participation explain individual market participation. |
| Keywords: | speculative bubbles, greater fool, behavioral economics, experimental finance |
| JEL: | C91 C92 G12 G41 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:inn:wpaper:2024-09 |
| By: | Bell, Clive (Heidelberg University); Gersbach, Hans (ETH Zurich); Haller, Hans (Virginia Tech) |
| Abstract: | When formal insurance is unavailable, mutual insurance among households can serve as an alternative. This paper analyzes a game between economic agents facing uncertainty and maximizing discounted utility without enforceable contracts or access to capital markets. While autarky is always a possible outcome, under high discount factors, a mutually beneficial trigger-strategy equilibrium can be achieved. Full insurance is possible with strongly negatively correlated endowments, while partial insurance is generally feasible. The analysis highlights environments wherein varying levels of insurance can emerge, with applications to real-world institutional contexts. |
| Keywords: | mutual insurance, risk sharing, group formation |
| JEL: | C72 C73 D80 G20 O11 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17406 |
| By: | Mustapha Nyenye Issah |
| Abstract: | We explore how dynamic entry deterrence operates through feedback strategies in markets experiencing stochastic demand fluctuations. The incumbent firm, aware of its own cost structure, can deter a potential competitor by strategically adjusting prices. The potential entrant faces a one-time, irreversible decision to enter the market, incurring a fixed cost, with profits determined by market conditions and the incumbent's hidden type. Market demand follows a Chan-Karolyi-Longstaff-Sanders Brownian motion. If the demand is low, the threat of entry diminishes, making deterrence less advantageous. In equilibrium, a weak incumbent may be incentivized to reveal its type by raising prices. We derive an optimal equilibrium using path integral control, where the entrant enters once demand reaches a high enough level, and the weak incumbent mixes strategies between revealing itself when demand is sufficiently low. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.16203 |
| By: | Beshkar, Mostafa (Department of Economics, Indiana University); Chang, Pao-Li (School of Economics, Singapore Management University); Song, Shenxi (Lazada South East Asia) |
| Abstract: | This paper introduces a quantitative framework to analyze the WTO’s reciprocity principle. Utilizing two polar bargaining environments, we measure terms-of-trade concessions among WTO members and examine how shifts in applied tariffs and economic fundamentals affect bilateral and multilateral balance of concessions. We find significant disparities in concessions, largely driven by the rise in trade imbalances since the early 1990s. Notably, although US-China bilateral tariffs suggest considerable terms-of-trade benefits for China, under a hypothetical balanced trade scenario, their relationship evolves towards near reciprocity following China’s accession to the WTO. Furthermore, in contrast to the significant gains in its relationship with the US, China experiences a terms-of-trade loss in its bilateral relationships with other WTO members. Lastly, we offer insights into the magnitude of concessions exchanged by countries at different levels of development. |
| JEL: | C51 C54 F13 F14 F15 |
| Date: | 2024–05–30 |
| URL: | https://d.repec.org/n?u=RePEc:ris:smuesw:2024_005 |
| By: | Li, Jiangtao (Singapore Management University); Wang, Kexin (Singapore Management University) |
| Abstract: | We study the design of mechanisms when the mechanism designer faces local uncertainty about agents’ beliefs. Specifically, we consider a designer who does not know the exact beliefs of the agents but is confident that her estimate is within of the beliefs held by the agents (where reflects the degree of local uncertainty). Adopting the robust optimization approach, we design mechanisms that incentivize agents to truthfully report their payoff-relevant information regardless of their actual beliefs. For any fixed, we identify necessary and sufficient conditions under which requiring this sense of robustness is without loss of revenue for the designer. By analyzing the limiting case in which approaches 0, we provide two rationales for the widely studied Bayesian mechanism design framework. |
| Date: | 2024–08–12 |
| URL: | https://d.repec.org/n?u=RePEc:ris:smuesw:2024_008 |
| By: | Gonzalez, Alejandro |
| Abstract: | I develop a Keynesian growth model where conflict over income distribution determines the labor share. Changes in workers’ bargaining power can either raise or depress output, depending on their effects on aggregate demand. An increase in demand reduces slack in the labor market, leading to a higher labor share. I incorporate the empirical implications of the model into a structural vector autoregression (SVAR) with sign restrictions to assess whether shocks to workers’ bargaining power raise or depress output, and to decompose the long-run decline in the labor share into components driven by demand, technology, and bargaining power. I find that an increase in labor’s bargaining power is contractionary in the short run, accounting for a quarter of output fluctuations. Demand shocks explain over 60% of the long-run decline in the labor share, with changes in labor’s bargaining power accounting for the remainder. |
| Date: | 2024–10–14 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:78kad |