nep-gth New Economics Papers
on Game Theory
Issue of 2021‒06‒28
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Trading with the Crowd By Eyal Neuman; Moritz Vo{\ss}
  2. The Bargaining Set and Coalition Formation By Ken-Ichi Shimomura
  3. Preference revelation games and strict cores of multiple-type housing market problems By Di Feng; Bettina Klaus
  4. Mean Field Portfolio Games in Incomplete Markets: Nonconstant Equilibria Do Not Exist in $L^\infty$ By Guanxing Fu; Chao Zhou
  5. Stability of collusion and quality differentiation- a Nash bargaining approach By Thanos Athanasopoulos; Burak Dindaroglu; Georgios Petropoulos
  6. Exploration-Exploitation in Multi-Agent Competition: Convergence with Bounded Rationality By Stefanos Leonardos; Georgios Piliouras; Kelly Spendlove
  7. From Griefing to Stability in Blockchain Mining Economies By Yun Kuen Cheung; Stefanos Leonardos; Georgios Piliouras; Shyam Sridhar
  8. Group-identity and long-run cooperation: an experiment By Gabriele Camera; Lukas Hohl
  9. Inequality aversion with general payoff function By Daijiro Kawanaka
  10. Differentiated goods in a dynamic Cournot duopoly with emission charges on outputs By Ahmad Naimzada; Marina Pireddu
  11. Lords and Vassals: Power, Patronage, and the Emergence of Inequality By Akerlof, Robert; Li, Hongyi; Yeo, Jonathan
  12. Driving a Hard Bargain is a Balancing Act: How social preferences constrain the negotiation process By Engler, Yola; Page, Lionel
  13. Unbiased Self-Play By Shohei Ohsawa
  14. Artificial Intelligence, Ethics, and Intergenerational Responsibility By Victor Klockmann; Alicia von Schenk; Marie Villeval
  15. Games in the Time of COVID-19: Promoting Mechanism Design for Pandemic Response By Bal\'azs Pej\'o; Gergely Bicz\'ok
  16. Equilibrium Effects of Pay Transparency By Zoe B. Cullen; Bobak Pakzad-Hurson
  17. Testing the sender: When signaling is not enough By Nicolás Figueroa; Carla Guadalupi
  18. Alternative Microfoundations for Strategic Classification By Meena Jagadeesan; Celestine Mendler-D\"unner; Moritz Hardt
  19. Positional Preferences and Efficiency in a Dynamic Economy By Aronsson, Thomas; Ghosh, Sugata; Wendner, Ronald
  20. Stockpiling and Shortages (the “Toilet Paper Paper") By Klumpp, Tilman
  21. Proof-of-Work Cryptocurrencies: Does Mining Technology Undermine Decentralization? By Agostino Capponi; Sveinn Olafsson; Humoud Alsabah

  1. By: Eyal Neuman; Moritz Vo{\ss}
    Abstract: We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with taking into account a common general price predicting signal. The unique Nash-equilibrium strategies reveal how each agent's liquidation policy adjusts the predictive trading signal to the aggregated transient price impact induced by all other agents. This unfolds a quantitative relation between trading signals and the order flow in crowded markets. We also formulate and solve the corresponding mean field game in the limit of infinitely many agents. We prove that the equilibrium trading speed and the value function of an agent in the finite $N$-player game converges to the corresponding trading speed and value function in the mean field game at rate $O(N^{-2})$. In addition, we prove that the mean field optimal strategy provides an approximate Nash-equilibrium for the finite-player game.
    Date: 2021–06
  2. By: Ken-Ichi Shimomura (Research Institute for Economics and Business Administration(RIEB), Kobe University, JAPAN)
    Abstract: We address the problem of predicting how rational agents will form coalitions in a nontransferable utility game, and within each coalition how they will allocate the gains obtained through cooperation. To answer these questions, we propose solution concepts according to which the coalition structure and the payoff allocations are simultaneously determined. We prove the nonemptiness and partial efficiency of the steady bargaining set, a refinement of the Zhou bargaining set, for at least one coalition structure under the restrictive non-crossing condition. In addition, we show the nonemptiness and possible inefficiency of the Mas-Colell bargaining set if this condition is not assumed.
    Keywords: Nontransferable utility game; Coalition structure; Bargaining set; Restrictive non-crossing condition
    JEL: C71 D71
    Date: 2021–06
  3. By: Di Feng; Bettina Klaus
    Abstract: We consider multiple-type housing market problems as introduced by Moulin (1995) and study the relationship between strict strong Nash equilibria and the strict core (two solution concepts that are defined in terms of the absence of weak blocking coalitions). We prove that for lexicographically separable preferences, the set of all strict strong Nash equilibrium outcomes of each preference revelation game that is induced by a strictly core-stable mechanism is a subset of the strict core, but not vice versa, i.e., there are strict core allocations that cannot be implemented in strict strong Nash equilibrium (Theorem 1). This result is extended to a more general set of preference domains that satisfy strict core non-emptiness and a minimal preference domain richness assumption (Theorem 2).
    Keywords: multiple-type housing market problems, strict core, strict strong Nash equilibria
    JEL: C71 C72 C78
    Date: 2021–06
  4. By: Guanxing Fu; Chao Zhou
    Abstract: We study mean field portfolio games in incomplete markets with random market parameters, where each player is concerned with not only her own wealth but also the relative performance to her competitors. We use the martingale optimality principle approach to characterize the unique Nash equilibrium in terms of a mean field FBSDE with quadratic growth, which is solvable under a weak interaction assumption. Motivated by the weak interaction assumption, we establish an asymptotic expansion result in powers of the competition parameter. When the market parameters do not depend on the Brownian paths, we get the Nash equilibrium in closed form. Moreover, when all the market parameters become time-independent, we revisit the games in [21] and our analysis shows that nonconstant equilibria do not exist in $L^\infty$, and the constant equilibrium obtained in [21] is unique in $L^\infty$, not only in the space of constant equilibria.
    Date: 2021–06
  5. By: Thanos Athanasopoulos; Burak Dindaroglu; Georgios Petropoulos
    Abstract: How do incentives to collude depend on how asymmetric firms are? In many markets, product quality is an important parameter that determines firms’ market strategies. We study collusion in a quality-differentiated duopoly and we adopt a Nash bargaining approach to compute the collusive equilibrium and assess its stability. We derive collusive and deviation strategies as continuous functions of quality asymmetry. We obtain novel and surprising results. Stability of collusion is...
    Date: 2021–06
  6. By: Stefanos Leonardos; Georgios Piliouras; Kelly Spendlove
    Abstract: The interplay between exploration and exploitation in competitive multi-agent learning is still far from being well understood. Motivated by this, we study smooth Q-learning, a prototypical learning model that explicitly captures the balance between game rewards and exploration costs. We show that Q-learning always converges to the unique quantal-response equilibrium (QRE), the standard solution concept for games under bounded rationality, in weighted zero-sum polymatrix games with heterogeneous learning agents using positive exploration rates. Complementing recent results about convergence in weighted potential games, we show that fast convergence of Q-learning in competitive settings is obtained regardless of the number of agents and without any need for parameter fine-tuning. As showcased by our experiments in network zero-sum games, these theoretical results provide the necessary guarantees for an algorithmic approach to the currently open problem of equilibrium selection in competitive multi-agent settings.
    Date: 2021–06
  7. By: Yun Kuen Cheung; Stefanos Leonardos; Georgios Piliouras; Shyam Sridhar
    Abstract: We study a game-theoretic model of blockchain mining economies and show that griefing, a practice according to which participants harm other participants at some lesser cost to themselves, is a prevalent threat at its Nash equilibria. The proof relies on a generalization of evolutionary stability to non-homogeneous populations via griefing factors (ratios that measure network losses relative to deviator's own losses) which leads to a formal theoretical argument for the dissipation of resources, consolidation of power and high entry barriers that are currently observed in practice. A critical assumption in this type of analysis is that miners' decisions have significant influence in aggregate network outcomes (such as network hashrate). However, as networks grow larger, the miner's interaction more closely resembles a distributed production economy or Fisher market and its stability properties change. In this case, we derive a proportional response (PR) update protocol which converges to market equilibria at which griefing is irrelevant. Convergence holds for a wide range of miners risk profiles and various degrees of resource mobility between blockchains with different mining technologies. Our empirical findings in a case study with four mineable cryptocurrencies suggest that risk diversification, restricted mobility of resources (as enforced by different mining technologies) and network growth, all are contributing factors to the stability of the inherently volatile blockchain ecosystem.
    Date: 2021–06
  8. By: Gabriele Camera (Economic Science Institute, Chapman University and DSE, University of Bologna); Lukas Hohl (University of Basel)
    Abstract: We stress-test the limits of the power of group identity in the context of cooperation by constructing laboratory economies where participants confront an indefinitely repeated social dilemma as strangers. Group identity is artificially induced by ran-dom assignment to color-coded groups, and reinforced by an initial cooperation task played in-group and in fixed pairs. Subsequently subjects interact in-group and out-group in large economies, as strangers. Indefinite repetition guarantees full cooperation is an equilibrium. Decision-makers can discriminate based on group aÿliation, but cannot observe past behaviors. We find no evidence of group biases. This suggests that group e ects are less likely to emerge when players cannot easily observe and compare characteristics on which to base categorizations and behaviors.
    Keywords: large groups, indefinitely repeated game, social norms
    JEL: C70 C90 D03
    Date: 2021
  9. By: Daijiro Kawanaka (Graduate School of Economics, Osaka University)
    Abstract: In the existing axiomatic models of inequity aversion, players have linear payoff functions, so they can predict that a dictator chooses only a completely selfish or completely fair offer in dictator games. However, experimental literature documents that a significantly amount of dictators offers 20-30% of the total pie to the passive opponent. This note, in contrast, axiomatizes inequity averse representation with general payoff function, so that we can explain such interior choices.
    Keywords: Inequality aversion under risk, Maxmin expected utility, Social preferences
    JEL: C72 D71 D81
    Date: 2021–06
  10. By: Ahmad Naimzada; Marina Pireddu
    Abstract: We extend the dynamic Cournot duopoly framework with emission charges on outputs by Mamada and Perrings (2020), which encompassed homogeneous products in its original formulation, to the more general case of differentiated goods, in order to highlight the richness in its static and dynamic outcomes. In the model each firm is taxed proportionally to its own emission only and charge functions are quadratic. Moreover, due to an adjustment capacity constraint, firms partially modify their output level toward the best response. Like it happened in Mamada and Perrings (2020), the only model steady state coincides with the Nash equilibrium. We find that the full efficacy of the environmental policy, which applies to an equilibrium that is globally asymptotically stable anytime it is admissible, is achieved in the case of independent goods, as well as with a low interdependence degree between goods in absolute value, independently of being substitutes or complements. On the other hand, when goods are substitutes and their interdependence degree is high, the considered environmental policy is still able to reduce pollution at the equilibrium, but the latter is stable just when the policy intensity degree is high enough. When instead goods are complements and their interdependence degree is high in absolute value, the considered environmental policy produces detrimental effects on the pollution level and the unique equilibrium is always unstable, when admissible. This highlights that, from a static viewpoint, even in the absence of free riding possibilities, the choice of the mechanism to implement has to be carefully pondered, according to the features of the considered economy.
    Keywords: dynamic Cournot duopoly, differentiated products, emission charges, pollution control, comparative statics, stability analysis.
    JEL: C62 D43 Q51 Q58
    Date: 2021–06
  11. By: Akerlof, Robert; Li, Hongyi; Yeo, Jonathan
    Abstract: This paper uses a laboratory experiment to study competitions for power-and the role of patronage in such competitions. We construct and analyze a new game-the "chicken-and-egg game"-in which chickens correspond to positions of power and eggs are the game's currency. We find that power tends to accumulate, through a "power begets power" dynamic, in the hands of "lords." Other subjects behave like their vassals in the sense that they take lords' handouts rather than compete against them. We observe substantial wealth inequality as well as power inequality. There are also striking gender differences in outcomes-particularly in rates of lordship. In a second treatment, where we eliminate patronage by knocking out the ability to transfer eggs, inequality is vastly reduced and the "power begets power" dynamic disappears.
    Keywords: gender differences; inequality; institutions; patronage; Power
    JEL: D02 D31 D72 J16 O10
    Date: 2020–05
  12. By: Engler, Yola; Page, Lionel
    Abstract: We investigate the haggling process in bargaining. Using an experimental bargaining game, we find that a first offer has a significant impact on the bargaining outcome even if it is costless to reject. First offers convey information on the player’s reservation value induced by his social preferences. They are most often accepted when they are not above the equal split. However, offers which request much more than the equal split induce punishing counteroffers. The bargaining outcome is therefore critically influenced by the balance of toughness and kindness signaled through the offers made in the haggling phase.
    Date: 2021–06–08
  13. By: Shohei Ohsawa
    Abstract: We present a general optimization framework for emergent belief-state representation without any supervision. We employed the common configuration of multiagent reinforcement learning and communication to improve exploration coverage over an environment by leveraging the knowledge of each agent. In this paper, we obtained that recurrent neural nets (RNNs) with shared weights are highly biased in partially observable environments because of their noncooperativity. To address this, we designated an unbiased version of self-play via mechanism design, also known as reverse game theory, to clarify unbiased knowledge at the Bayesian Nash equilibrium. The key idea is to add imaginary rewards using the peer prediction mechanism, i.e., a mechanism for mutually criticizing information in a decentralized environment. Numerical analyses, including StarCraft exploration tasks with up to 20 agents and off-the-shelf RNNs, demonstrate the state-of-the-art performance.
    Date: 2021–06
  14. By: Victor Klockmann (Goethe-University Frankfurt am Main, Max Planck Institute for Human Development - Max-Planck-Gesellschaft); Alicia von Schenk (Goethe-University Frankfurt am Main, Max Planck Institute for Human Development - Max-Planck-Gesellschaft); Marie Villeval (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon, IZA - Forschungsinstitut zur Zukunft der Arbeit - Institute of Labor Economics)
    Abstract: Humans shape the behavior of artificially intelligent algorithms. One mechanism is the training these systems receive through the passive observation of human behavior and the data we constantly generate. In a laboratory experiment with a sequence of dictator games, we let participants' choices train an algorithm. Thereby, they create an externality on future decision making of an intelligent system that affects future participants. We test how information on training artificial intelligence affects the prosociality and selfishness of human behavior. We find that making individuals aware of the consequences of their training on the well-being of future generations changes behavior, but only when individuals bear the risk of being harmed themselves by future algorithmic choices. Only in that case, the externality of artificially intelligence training induces a significantly higher share of egalitarian decisions in the present.
    Keywords: Artificial Intelligence,Morality,Prosociality,Generations,Externalities
    Date: 2021
  15. By: Bal\'azs Pej\'o; Gergely Bicz\'ok
    Abstract: Most governments employ a set of quasi-standard measures to fight COVID-19 including wearing masks, social distancing, virus testing, contact tracing, and vaccination. However, combining these measures into an efficient holistic pandemic response instrument is even more involved than anticipated. We argue that some non-trivial factors behind the varying effectiveness of these measures are selfish decision-making and the differing national implementations of the response mechanism. In this paper, through simple games, we show the effect of individual incentives on the decisions made with respect to mask wearing, social distancing and vaccination, and how these may result in sub-optimal outcomes. We also demonstrate the responsibility of national authorities in designing these games properly regarding data transparency, the chosen policies and their influence on the preferred outcome. We promote a mechanism design approach: it is in the best interest of every government to carefully balance social good and response costs when implementing their respective pandemic response mechanism; moreover, there is no one-size-fits-all solution when designing an effective solution.
    Date: 2021–06
  16. By: Zoe B. Cullen; Bobak Pakzad-Hurson
    Abstract: The public discourse around pay transparency has focused on the direct effect: how workers seek to rectify newly-disclosed pay inequities through renegotiations. The question of how wage-setting and hiring practices of the firm respond in equilibrium has received less attention. To study these outcomes, we build a model of bargaining under incomplete information and test our predictions in the context of the U.S. private sector. Our model predicts that transparency reduces the individual bargaining power of workers, leading to lower average wages. A key insight is that employers credibly refuse to pay high wages to any one worker to avoid costly renegotiations with others under transparency. In situations where workers do not have individual bargaining power, such as under a collective bargaining agreement or in markets with posted wages, greater transparency has a muted impact on average wages. We test these predictions by evaluating the roll-out of U.S. state legislation protecting the right of workers to inquire about the salaries of their coworkers. Consistent with our prediction, the laws lead wages to decline by approximately 2% overall, but declines are progressively smaller in occupations with higher unionization rates. Our model provides a unified framework to analyze a wide range of transparency policies, and reconciles effects of transparency mandates documented in a variety of countries and contexts.
    JEL: C78 D82 D83 J31 M52
    Date: 2021–06
  17. By: Nicolás Figueroa; Carla Guadalupi
    Abstract: We study signaling in the presence of endogenous information acquisition by the receiver. A firm, after observing the worker’s costly action, may acquire further information by performing a test on the applicant, and then decide to hire him. We consider different models of information acquisition, including the rational inattention, a generalization of the “truth or noise” and a general grading model. We study test effectiveness as function of beliefs generated through signaling by the worker, and provide clear-cut predictions on the complementarity/substitutability between costly information transmission (signaling) and acquisition, and its implications for the equilibrium. We first show that test effectiveness is non-monotone in beliefs. It exhibits increasing regions, where beliefs and test effectiveness act as complements, with higher beliefs inducing more effective tests, and decreasing regions in which higher beliefs crowd out the firm’s information acquisition. We then show that, when beliefs and test effectiveness are complements, the equilibrium involves (at least partial) separation between workers’ types. Since the high type is more willing to face a more exacting test than a low type, he will exert costly effort to improve the firm’s opinion. When beliefs and test effectiveness are substitutes, any signaling attempt by the high type will be mimicked by the low one who benefits more from relaxed standards and indiscriminate hiring, and the only plausible equilibrium involves both types pooling.
    Date: 2020
  18. By: Meena Jagadeesan; Celestine Mendler-D\"unner; Moritz Hardt
    Abstract: When reasoning about strategic behavior in a machine learning context it is tempting to combine standard microfoundations of rational agents with the statistical decision theory underlying classification. In this work, we argue that a direct combination of these standard ingredients leads to brittle solution concepts of limited descriptive and prescriptive value. First, we show that rational agents with perfect information produce discontinuities in the aggregate response to a decision rule that we often do not observe empirically. Second, when any positive fraction of agents is not perfectly strategic, desirable stable points -- where the classifier is optimal for the data it entails -- cease to exist. Third, optimal decision rules under standard microfoundations maximize a measure of negative externality known as social burden within a broad class of possible assumptions about agent behavior. Recognizing these limitations we explore alternatives to standard microfoundations for binary classification. We start by describing a set of desiderata that help navigate the space of possible assumptions about how agents respond to a decision rule. In particular, we analyze a natural constraint on feature manipulations, and discuss properties that are sufficient to guarantee the robust existence of stable points. Building on these insights, we then propose the noisy response model. Inspired by smoothed analysis and empirical observations, noisy response incorporates imperfection in the agent responses, which we show mitigates the limitations of standard microfoundations. Our model retains analytical tractability, leads to more robust insights about stable points, and imposes a lower social burden at optimality.
    Date: 2021–06
  19. By: Aronsson, Thomas; Ghosh, Sugata; Wendner, Ronald
    Abstract: Based on an endogenous growth model, this paper characterizes the conditions under which positional preferences do not give rise to intertemporal distortions as well as derives an optimal tax policy response in cases where these conditions are not satisfied. In our model, individuals can be positional both in terms of their consumption and wealth, the relative concerns partly reflect comparisons with people in other countries, and we distinguish between a (conventional) welfarist government and a paternalist government that does not respect positional preferences. We also extend the analysis to a multi-country framework and show that Nash-competition among local paternalist governments leads to a global social optimum, whereas Nash-competition among local welfarist governments does not.
    Keywords: Positional preferences, efficiency, intertemporal distortions, welfarist government, paternalist government, endogenous growth
    JEL: D62 E61 H11 O43
    Date: 2020–01–30
  20. By: Klumpp, Tilman (University of Alberta, Department of Economics)
    Abstract: Widespread stockpiling of everyday household items (e.g., toilet paper) occurred in the wake of the Covid-19 pandemic, resulting in shortages of these items in stores. Both phenomena reinforce each other: The expectation of shortages causes stockpiling behavior, which in turn amplifies the shortages, which in turn encourages more stockpiling. In this paper, I examine this feedback loop. In the model, households want to consume one unit of a good per period, but can store more than one unit at a cost. Aggregate supply of the good may be insufficient to meet aggregate demand, but prices cannot adjust to equate supply and demand. I characterize stationary equilibria in which households maintain target inventories of z units. Thus, stockpiling arises if z > 1, and I demonstrate that this can be an equilibrium even for very small aggregate supply-demand imbalances. In particular, in many equilibria the incentive to stockpile is driven mostly by the stockpiling behavior of other households, and not by the fundamental supply shortage. Transitional dynamics are examined as well.
    Keywords: storage; consumer inventories; stockpiling; multiple equilibria; rationing; mean field games; search models
    JEL: C61 C62 C73 D15
    Date: 2021–06–23
  21. By: Agostino Capponi; Sveinn Olafsson; Humoud Alsabah
    Abstract: Does the proof-of-work protocol serve its intended purpose of supporting decentralized cryptocurrency mining? To address this question, we develop a game-theoretical model where miners first invest in hardware to improve the efficiency of their operations, and then compete for mining rewards in a rent-seeking game. We argue that because of capacity constraints faced by miners, centralization in mining is lower than indicated by both public discourse and recent academic work. We show that advancements in hardware efficiency do not necessarily lead to larger miners increasing their advantage, but rather allow smaller miners to expand and new miners to enter the competition. Our calibrated model illustrates that hardware efficiency has a small impact on the cost of attacking a network, while the mining reward has a significant impact. This highlights the vulnerability of smaller and emerging cryptocurrencies, as well as of established cryptocurrencies transitioning to a fee-based mining reward scheme.
    Date: 2021–06

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