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on Game Theory |
| By: | Wang Zhijian |
| Abstract: | People choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. The process can be modelled as an evolutionary game dynamics system, which may be controllable. In modern control theory, eigenvalue (pole) assignment is a basic approach to designing a full-state feedback controller, which can influence the outcome of a game. This study shows that, in a game with two Nash equilibria, the long-running strategy distribution can be controlled by pole assignment. We illustrate a theoretical workflow to design and evaluate the controller. To our knowledge, this is the first realisation of the control of equilibrium selection by design in the game dynamics theory paradigm. We hope the controller can be verified in a laboratory human subject game experiment. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.09131&r=gth |
| By: | Benjamin Golub; Yu-Chi Hsieh; Evan Sadler |
| Abstract: | Bolletta (2021, Math. Soc. Sci. 114:1-10) studies a model in which a network is strategically formed and then agents play a linear best-response investment game in it. The model is motivated by an application in which people choose both their study partners and their levels of educational effort. Agents have different one-dimensional types $\unicode{x2013}$ private returns to effort. A main result claims that pairwise Nash stable networks have a locally complete structure consisting of possibly overlapping cliques: if two agents are linked, they are part of a clique composed of all agents with types between theirs. We offer a counterexample showing that the claimed characterization is incorrect, highlight where the analysis errs, and discuss implications for network formation models. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.05831&r=gth |
| By: | Deepanshu Vasal |
| Abstract: | In this paper, we consider a mean field model of social behavior where there are an infinite number of players, each of whom observes a type privately that represents her preference, and publicly observes a mean field state of types and actions of the players in the society. The types (and equivalently preferences) of the players are dynamically evolving. Each player is fully rational and forward-looking and makes a decision in each round t to buy a product. She receives a higher utility if the product she bought is aligned with her current preference and if there is a higher fraction of people who bought that product (thus a game of strategic complementarity). We show that for certain parameters when the weight of strategic complementarity is high, players eventually herd towards one of the actions with probability 1 which is when each player buys a product irrespective of her preference. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.03303&r=gth |
| By: | Darpö, Erik; Domínguez, Alvaro; Martín-Rodríguez, María |
| Abstract: | We present a model analyzing the endogenous network formation prior to an infinite-horizon network bargaining game. We assume agents of two types with either one of two alternatives: connections among players of the same type are cheaper than among players of different type or vice versa. In this way, players not only need to consider the trade-off between more outside options and the costs of maintaining those additional links, but also what type of players they connect to. We characterize pairwise stable network structures through necessary and sufficient conditions, highlighting the role played by the way in which heterogeneous nodes are placed in the different components for the pairwise stability of the networks. Finally, we perform a welfare analysis, comparing the efficient structures with those that are stable. |
| Keywords: | Bargaining, Heterogeneity, Network formation, C72, C78, D85 |
| Date: | 2023–01 |
| URL: | http://d.repec.org/n?u=RePEc:agi:wpaper:00000260&r=gth |
| By: | Hongcheng Li |
| Abstract: | This paper models a multiplayer war of attrition game with asymmetric incomplete information on the private provision of one public good to investigate the effect of ex-ante asymmetry. In the unique equilibrium, asymmetry leads to a stratified behavior pattern such that one player provides the good instantly with a positive probability, while each of the others has no probability of provision before a certain moment which is idiosyncratic. Comparative statics show that one with less patience, lower cost of provision, and higher reputation in valuation provides uniformly faster. The cost of delay is mainly determined by the strongest type, namely the highest type of the instant-exit player. This paper considers two types of introduction of asymmetry: raising the strongest type tends to improve efficiency, whereas controlling the strongest type aligns the effect of asymmetry with the sign of an intuitive measure of the cost of symmetry. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.09427&r=gth |
| By: | Giovanni Andreottola (Vienna University of Economics and Business (WU) and CSEF); Elia Sartori (CSEF) |
| Abstract: | We study the use of simplistic arguments in political communication, developing a novel model of mobilization through rhetoric with naive and sophisticated voters. We show that politicians sometimes choose simplistic arguments in order to appear more competent, exploiting what we call Poe’s Law, that is, the uncertainty on whether the argument used by the politician reflects her own competence or is ‘degraded’ to meet the demand for simplistic arguments of the naive electorate. We compare the Bayes Nash game with a game in which sophisticated voters are unable to conceptualize Poe’s Law, dismissing their peers’ cognitive abilities and identifying with a leader that speaks to a fully naive crowd. The two games have opposed predictions on how expected simplism departs from its demand-driven benchmark, as well as on the interpretation of extreme arguments. Our results demonstrate that dismissal is a valid rationalization of an overly simplistic political debate. |
| Keywords: | Simplistic rhetoric, Dismissal, Poe’s Law, Populism. |
| JEL: | D72 D82 D83 D91 |
| Date: | 2023–02–17 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:668&r=gth |
| By: | Vijay V. Vazirani |
| Abstract: | LP-duality theory has played a central role in the study of the core, right from its early days to the present time. The 1971 paper of Shapley and Shubik, which gave a characterization of the core of the assignment game, has been a paradigm-setting work in this regard. However, despite extensive follow-up work, basic gaps still remain. We address these gaps using the following building blocks from LP-duality theory: 1). Total unimodularity (TUM). 2). Complementary slackness conditions and strict complementarity. TUM plays a vital role in the Shapley-Shubik theorem. We define several generalizations of the assignment game whose LP-formulations admit TUM; using the latter, we characterize their cores. The Hoffman-Kruskal game is the most general of these. Its applications include matching students to schools and medical residents to hospitals, and its core imputations provide a way of enforcing constraints arising naturally in these applications: encouraging diversity and discouraging over-representation. Complementarity enables us to prove new properties of core imputations of the assignment game and its generalizations. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.07627&r=gth |
| By: | Yurong Chen; Xiaotie Deng; Jiarui Gan; Yuhao Li |
| Abstract: | It is shown in recent studies that in a Stackelberg game the follower can manipulate the leader by deviating from their true best-response behavior. Such manipulations are computationally tractable and can be highly beneficial for the follower. Meanwhile, they may result in significant payoff losses for the leader, sometimes completely defeating their first-mover advantage. A warning to commitment optimizers, the risk these findings indicate appears to be alleviated to some extent by a strict information advantage the manipulations rely on. That is, the follower knows the full information about both players' payoffs whereas the leader only knows their own payoffs. In this paper, we study the manipulation problem with this information advantage relaxed. We consider the scenario where the follower is not given any information about the leader's payoffs to begin with but has to learn to manipulate by interacting with the leader. The follower can gather necessary information by querying the leader's optimal commitments against contrived best-response behaviors. Our results indicate that the information advantage is not entirely indispensable to the follower's manipulations: the follower can learn the optimal way to manipulate in polynomial time with polynomially many queries of the leader's optimal commitment. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.11829&r=gth |
| By: | Jorge Alcalde-Unzu; Oihane Gallo; Elena Inarra; Juan D. Moreno-Ternero |
| Abstract: | Agents may form coalitions. Each coalition shares its endowment among its agents by applying a sharing rule. The sharing rule induces a coalition formation problem by assuming that agents rank coalitions according to the allocation they obtain in the corresponding sharing problem. We characterize the sharing rules that induce a class of stable coalition formation problems as those that satisfy a natural axiom that formalizes the principle of solidarity. Thus, solidarity becomes a sufficient condition to achieve stability. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.07618&r=gth |
| By: | Toru Kitagawa; Guanyi Wang |
| Abstract: | Designing individualized allocation of treatments so as to maximize the equilibrium welfare of interacting agents has many policy-relevant applications. Focusing on sequential decision games of interacting agents, this paper develops a method to obtain optimal treatment assignment rules that maximize a social welfare criterion by evaluating stationary distributions of outcomes. Stationary distributions in sequential decision games are given by Gibbs distributions, which are difficult to optimize with respect to a treatment allocation due to analytical and computational complexity. We apply a variational approximation to the stationary distribution and optimize the approximated equilibrium welfare with respect to treatment allocation using a greedy optimization algorithm. We characterize the performance of the variational approximation, deriving a performance guarantee for the greedy optimization algorithm via a welfare regret bound. We establish the convergence rate of this bound. We demonstrate the performance of our proposed method in simulation exercises. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.05747&r=gth |
| By: | Ayca Kaya (University of Miami); Santanu Roy (Southern Methodist University) |
| Abstract: | We analyze the effect of transparency of past trading volumes in markets where an informed long-lived seller can repeatedly trade with short-lived uninformed buyers. Transparency allows buyers to observe previously sold quantities. In markets with intra-period monopsony (single buyer each period), transparency reduces welfare if the ex-ante expected quality is low, but improves welfare if the expected quality is high. The effect is reversed in markets with intra-period competition (multiple buyers each period). This discrepancy in the efficiency implications of transparency is explained by how buyer competition affects the seller's ability to capture rents, which, in turn, influences market screening. |
| Keywords: | Repeated sales, adverse selection, transparency, competition, market efficiency |
| JEL: | D82 C73 D61 |
| Date: | 2023–01 |
| URL: | http://d.repec.org/n?u=RePEc:smu:ecowpa:2301&r=gth |
| By: | Avila, Piret; Mullon, Charles |
| Abstract: | Evolutionary game theory and the adaptive dynamics approach have made invaluable contributions to understand how gradual evolution leads to adaptation when individuals interact. Here, we review some of the basic tools that have come out of these contributions to model the evolution of quantitative traits in complex populations. We collect together mathematical expressions that describe directional and disruptive selection in class- and group-structured populations in terms of individual fitness, with the aims of bridging different models and interpreting selection. In particular, our review of disruptive selection suggests there are two main paths that can lead to diversity: (i) when individual fitness increases more than linearly with trait expression; (ii) when trait expression simultaneously increases the probability that an individual is in a certain context (e.g. a given age, sex, habitat, size or social environment) and fitness in that context. We provide various examples of these and more broadly argue that population structure lays the ground for the emergence of polymorphism with unique characteristics. Beyond this, we hope that the descriptions of selection we present here help see the tight links among fundamental branches of evolutionary biology, from life-history to social evolution through evolutionary ecology, and thus favour further their integration. |
| Date: | 2023–03–06 |
| URL: | http://d.repec.org/n?u=RePEc:tse:iastwp:127397&r=gth |
| By: | Paolo Bova; Alessandro Di Stefano; The Anh Han |
| Abstract: | In the context of rapid discoveries by leaders in AI, governments must consider how to design regulation that matches the increasing pace of new AI capabilities. Regulatory Markets for AI is a proposal designed with adaptability in mind. It involves governments setting outcome-based targets for AI companies to achieve, which they can show by purchasing services from a market of private regulators. We use an evolutionary game theory model to explore the role governments can play in building a Regulatory Market for AI systems that deters reckless behaviour. We warn that it is alarmingly easy to stumble on incentives which would prevent Regulatory Markets from achieving this goal. These 'Bounty Incentives' only reward private regulators for catching unsafe behaviour. We argue that AI companies will likely learn to tailor their behaviour to how much effort regulators invest, discouraging regulators from innovating. Instead, we recommend that governments always reward regulators, except when they find that those regulators failed to detect unsafe behaviour that they should have. These 'Vigilant Incentives' could encourage private regulators to find innovative ways to evaluate cutting-edge AI systems. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.03174&r=gth |
| By: | Lucila Porto |
| Abstract: | What if Q-Learning algorithms set not only prices but also the degree of differentiation between them? In this paper, I tackle this question by analyzing the competition between two Q-Learning algorithms in a Hotelling setting. I find that most of the simulations converge to a Nash Equilibrium where the algorithms are playing non-competitive strategies. In most simulations, they optimally learn not to differentiate each other and to set a collusive price. An underlying deviation and punishment scheme sustains this implicit agreement. The results are robust to the enlargement of the action space and the introduction of relocalization costs. |
| JEL: | L1 L4 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:aep:anales:4587&r=gth |
| By: | Yingkai Li; Xiaoyun Qiu |
| Abstract: | We study the distribution of multiple homogeneous items to multiple agents with unit demand. Monetary transfer is not allowed and the allocation of the items can only depend on the informative signals that are manipulable by costly and wasteful efforts. Examples of such scenarios include grant allocation, college admission, lobbying and affordable housing. We show that the welfare-maximizing mechanism takes the form of a contest and characterize it. We apply our characterizations to study large contests. When the number of agents is large compared to item(s), the format of the optimal contest converges to winner-takes-all, but principal's payoff does not. When both the number of items and agents are large, allocation is randomized to middle types to induce no effort under optimal contest, which weakly decreases effort for all higher types. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.09168&r=gth |
| By: | Ran Canetti; Amos Fiat; Yannai A. Gonczarowski |
| Abstract: | A powerful feature in mechanism design is the ability to irrevocably commit to the rules of a mechanism. Commitment is achieved by public declaration, which enables players to verify incentive properties in advance and the outcome in retrospect. However, public declaration can reveal superfluous information that the mechanism designer might prefer not to disclose, such as her target function or private costs. Avoiding this may be possible via a trusted mediator; however, the availability of a trusted mediator, especially if mechanism secrecy must be maintained for years, might be unrealistic. We propose a new approach to commitment, and show how to commit to, and run, any given mechanism without disclosing it, while enabling the verification of incentive properties and the outcome -- all without the need for any mediators. Our framework is based on zero-knowledge proofs -- a cornerstone of modern cryptographic theory. Applications include non-mediated bargaining with hidden yet binding offers. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.05590&r=gth |
| By: | Pan, Jingjing; Li, Jianbiao; Zhu, Chengkang |
| Abstract: | Although previous literature demonstrates that punishment is more efficient and stable than reward, in our daily life, numerous kinds of rewards permeate. One possible explanation for widely use of reward institution in practice is that it’s an efficient and satisfactory way to enhance cooperation and welfare in a social dilemma situation even the contribution is hardly evaluated accurately. Nevertheless, this explanation lacks support from empirical evidence. Our study aims to examine whether the institution with reward option is an efficient and satisfactory way to solve social dilemma problems under imperfect information conditions. We show that reward institutions sustain higher cooperation levels and let participants get more welfare under imperfect information conditions. Furthermore, we find most participants to have a tendency to favor reward institutions, even when the information is highly noisy. Our study sheds light on the superiority of reward institutions over punishment institutions in a realistic world. |
| Keywords: | Public goods games, Reward, Imperfect information, Cooperation, Welfare |
| JEL: | C91 C92 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:esprep:269216&r=gth |