nep-mic New Economics Papers
on Microeconomics
Issue of 2021‒05‒17
28 papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. Test Design under Falsification By Perez-Richet, Eduardo; Skreta, Vasiliki
  2. Perceived Competition in Networks By Bochet, Olivier; Faure, Mathieu; Long, Yan; Zenou, Yves
  3. Asymmetric Information and Delegated Selling By Janssen, Maarten; Roy, Santanu
  4. Toxic Types and Infectious Communication Breakdown By Eliaz, Kfir; Frug, Alexander
  5. Information Design by an Informed Designer By Koessler, Frederic; Skreta, Vasiliki
  6. The multiple-volunteers principle By Goldlücke, Susanne; Tröger, Thomas
  7. Contracting under Adverse Selection: Certifiable vs. Uncertifiable Information By Schmitz, Patrick W.
  8. Discovery and Equilibrium in Games with Unawareness By Burkhard C. Schipper
  9. Optimal Ownership of Public Goods under Asymmetric Information By Schmitz, Patrick W.
  10. A connections model with decreasing returns link-formation technology By Olaizola, Norma; Valenciano, Federico
  11. Correlation Robustly Optimal Auctions By Wanchang Zhang
  12. Optimally Imprecise Memory and Biased Forecasts By Azeredo da Silveira, Rava; Sung, Yeji; Woodford, Michael
  13. The Right to Quit Work: An Efficiency Rationale for Restricting the Freedom of Contract By Müller, Daniel; Schmitz, Patrick W.
  14. Dynamic Choices and Common Learning By Rahul Deb; Ludovic Renou
  15. Learning to agree over large state spaces By Michele Crescenzi
  16. Goal-oriented agents in a market By Inés Macho-Stadler; David Pérez-Castrillo; Nicolas Quérou
  17. Retrospective Search: Exploration and Ambition on Uncharted Terrain By Urgun, Can; Yariv, Leeat
  18. Auctions of Homogeneous Goods: A Case for Pay-as-Bid By Pycia, Marek; Woodward, Kyle
  19. Incentive contracts when agents distort probabilities By Víctor González-Jiménez
  20. Robust Bilateral Trade Mechanisms with Known Expectations By Wanchang Zhang
  21. Local Evidence and Diversity in Minipublics By Bardhi, Arjada; Bobkova, Nina
  22. Collective Brand Reputation By Nocke, Volker; Strausz, Roland
  23. Assignments with Ethical Concerns By Hitoshi Matsushima
  24. Confidence is good; too much, not so much: Exploring the effects on reward-based crowdfunding success By Naomi Moy; Ho Fai Chan; Frank Mathmann; Markus Schaffner; Benno Torgler
  25. Targeted product design By Bar-Isaac, Heski; Caruana, Guillermo; Cuñat, Vicente
  26. Search and Price Discrimination Online By Mauring, Eeva
  27. Exploiting rivals' strengths By Calzolari, Giacomo; Denicolò, Vincenzo
  28. Algorithmic collusion with imperfect monitoring By Calvano, Emilio; Calzolari, Giacomo; Denicolò, Vincenzo; Pastorello, Sergio

  1. By: Perez-Richet, Eduardo; Skreta, Vasiliki
    Abstract: We study the optimal design of tests with manipulable inputs: data, actions, reports. An agent can, at a cost, falsify the input into the test, or state of the world, so as to influence the downstream binary decision of a receiver informed by the test. We characterize receiver-optimal tests under different constraints. Under covert falsification, the receiver-optimal test is inefficient. With a rich state space, it involves equilibrium falsification at a possibly large cost to the agent, and may therefore exert a negative social externality. The receiver-optimal test that is immune to falsification, while also inefficient, strictly improves the payoff of the agent. When the falsification strategy of the agent is observable, or can be committed to, the receiver-optimal test is efficient, uses a rich signal space, and gives the receiver at least half of his full information payoff.
    Keywords: Bayesian persuasion; Cheating; Falsification; information design; manipulation; Tests
    JEL: C72 D82
    Date: 2021–01
  2. By: Bochet, Olivier; Faure, Mathieu; Long, Yan; Zenou, Yves
    Abstract: Agents compete for the same resources and are only aware of their direct neighbors in a network. We propose a new equilibrium concept, referred to as peer-consistent equilibrium (PCE). In a PCE, each agent chooses an effort level that maximizes her subjective perceived utility and the effort levels of all individuals in the network need to be consistent. We develop an algorithm that breaks the network into communities. We use this decomposition to completely characterize peer-consistent equilibria by identifying which sets of agents can be active in equilibrium. An agent is active if she either belongs to a strong community or if few agents are aware of her existence. We show that there is a unique stable PCE. We provide a microfoundation of eigenvector centrality, since, in any stable PCE, agents' effort levels are proportional to their eigenvector centrality in the network.
    Keywords: eigenvector centrality; policies; Social Networks
    JEL: C72 D85
    Date: 2020–12
  3. By: Janssen, Maarten; Roy, Santanu
    Abstract: Asymmetric information about product quality can create incentives for a privately informed manufacturer to sell to uninformed consumers through a retailer and to maintain secrecy of upstream pricing. Delegating retail price setting to an intermediary generates pooling equilibria that avoid signaling distortions associated with direct selling even under reasonable restrictions on beliefs; these beliefs can also prevent double marginalization by the retailer. Expected profit, consumer surplus and social welfare can all be higher with intermediated selling. However, if secrecy of upstream pricing cannot be maintained, selling through a retailer can only lower the expected profit of the manufacturer.
    Keywords: asymmetric information; delegation; intermediary; product quality; signaling
    JEL: D43 D82 L13 L15
    Date: 2020–12
  4. By: Eliaz, Kfir; Frug, Alexander
    Abstract: We introduce a new reason for why an informed sender may not be able to communicate(via cheap talk) his private information to an uninformed receiver. Our framework has two novel features: (i) conditional on interacting, both parties agree on the optimal action to take given the sender's information, and (ii) there are some sender types (the "toxic" types) with which the receiver prefers not to interact. Our main result establishes that for a broad class of preferences, any interval equilibrium (where each message is associated with an interval of types) induces only finitely many actions in the support of the receiver's strategy. For a canonical class of preferences with uniformly distributed types, we characterize the Pareto efficient(interval) equilibria and illustrate how communication is adversely affected even with a small set of toxic types. In addition, we show that introducing a second stage in which the receiver gets a noisy signal on the sender type can have a dramatic effect on the first-stage communication.
    Keywords: cheap talk; contagion
    JEL: D83
    Date: 2020–12
  5. By: Koessler, Frederic; Skreta, Vasiliki
    Abstract: A designer is privately informed about the state and chooses an information disclosure mechanism to influence the decisions of multiple agents playing a game. We define an intuitive class of incentive compatible information disclosure mechanisms which we coin interim optimal mechanisms. We prove that an interim optimal mechanism exists, and that it is an equilibrium outcome of the interim information design game. An ex-ante optimal mechanism may not be interim optimal, but it is whenever it is ex-post optimal. In addition, in leading settings in which action sets are binary, every ex-ante optimal mechanism is interim optimal. We relate interim optimal mechanisms to other solutions of informed principal problems.
    Keywords: Bayesian persuasion; core mechanism; Informed principal; interim information design; neutral optimum; strong-neologism proofness; verifiable types
    JEL: C72 D82
    Date: 2021–01
  6. By: Goldlücke, Susanne; Tröger, Thomas
    Abstract: We consider mechanisms for assigning an unpleasant task among a group of agents with heterogenous abilities. We emphasize threshold rules: every agent decides whether or not to ``volunteer''; if the number of volunteers exceeds a threshold number, the task is assigned to a random volunteer; if the number is below the threshold, the task is assigned to a random non-volunteer. We show that any non-extreme threshold rule allows for a symmetric equilibrium in which every ability type is strictly better off than in a random assignment. This holds for arbitrarily high costs of performing the task. Within the class of binary-action mechanisms, some threshold rule is utilitarian optimal. The first-best can be approximated arbitrarily closely with a threshold rule as the group size tends to infinity; that is, there exist threshold numbers such that with probability arbitrarily close to 1 the task is performed by an agent with an ability arbitrarily close to the highest possible ability. The optimal threshold number goes to infinity as the group size tends to infinity.
    Keywords: mechanism design without transfers; Public Good Provision; volunteering
    JEL: D82 H41
    Date: 2020–12
  7. By: Schmitz, Patrick W.
    Abstract: The analysis of adverse selection problems in seller-buyer relationships has typically been based on the assumption that private information is uncertifiable, while in practice it may well be certifiable. If a buyer has certifiable private information, he can conceal evidence, but he cannot claim to have information for which he has no evidence, so he has fewer possibilities to misrepresent his information. Nevertheless, we find that the expected total surplus can be strictly smaller in the case of certifiable information than in the case of uncertifiable information. This finding holds when the buyer may have private information with some exogenous probability as well as in the case of opportunistic information gathering, where the buyer can privately decide whether or not to acquire information for strategic reasons.
    Keywords: Adverse Selection; asymmetric information; Contracting; Information gathering; screening
    JEL: C73 D23 D82 D86 L24
    Date: 2020–12
  8. By: Burkhard C. Schipper (Department of Economics, University of California Davis)
    Abstract: Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are ``self-destroying'' as a player's representation of the game may change after playing it once. We define discovery processes where at each state there is an extensive-form game with unawareness that together with the players' play determines the transition to possibly another extensive-form game with unawareness in which players are now aware of actions that they have discovered. A discovery process is rationalizable if players play extensive-form rationalizable strategies in each game with unawareness. We show that for any game with unawareness there is a rationalizable discovery process that leads to a self-confirming game that possesses a self-confirming equilibrium in extensive-form rationalizable strategies. This notion of equilibrium can be interpreted as steady-state of both a discovery and learning process.
    Keywords: Self-confirming equilibrium, conjectural equilibrium, extensive-form rationalizability, unawareness, extensive-form games, equilibrium, learning, discovery
    JEL: C72 D83
    Date: 2021–05–05
  9. By: Schmitz, Patrick W.
    Abstract: Consider two parties who can make non-contractible investments in the provision of a public good. Who should own the physical assets needed to provide the public good? In the literature it has been argued that the party who values the public good most should be the owner, regardless of the investment technologies. Yet, this result has been derived under the assumption of symmetric information. We show that technology matters when the negotiations over the provision of the public good take place under asymmetric information. If party A has a better investment technology, ownership by party A can be optimal even when party B has a larger expected valuation of the public good.
    Keywords: incomplete contracts; control rights; public goods; private information; investment incentives
    JEL: D23 D82 D86 H41 L33
    Date: 2021
  10. By: Olaizola, Norma; Valenciano, Federico
    Abstract: We study a connections model where the strength of a link depends on the amount invested in it and is determined by an increasing strictly concave function. The revenue from investments in links is the information that the nodes receive through the network. First, the structures of efficient networks are characterized, and conditions for optimal investments constrained to supporting a given network are obtained. Second, assuming that links are the result of investments by the node-players involved, there is the question of stability. We introduce and characterize a notion of marginal equilibrium weaker than that of Nash equilibrium, and identify different marginally stable structures. Efficiency and stability are shown to be incompatible, but partial subsidizing is shown to be able to bridge the gap.
    Keywords: Networks, Connections model, Decreasing returns, Efficiency, Stability.
    JEL: A14 C72 D85
    Date: 2020–10–28
  11. By: Wanchang Zhang
    Abstract: We study the design of auction within the correlation-robust framework in which the auctioneer is assumed to have information only about marginal distributions, but does not know the correlation structure of the joint distribution. The performance of a mechanism is evaluated in the worst-case over the uncertainty of joint distributions that are consistent with the marginal distributions. For the two-bidder case, we characterize the Second Price Auction with Uniformly Distributed Reserves as a maxmin auction among dominant strategy incentive compatible (DSIC) and ex-post individually rational (EPIR) mechanisms under the robust-version regularity conditions. For the $N$-bidder ($N\ge 3$) case, we characterize the Second Price Auction with $Beta (\frac{1}{N-1},1)$ Distributed Reserves as a maxmin auction among exclusive (a bidder whose bid is not the highest will never be allocated) DSIC and EPIR mechanisms under the general robust-version regularity conditions (I).
    Date: 2021–05
  12. By: Azeredo da Silveira, Rava; Sung, Yeji; Woodford, Michael
    Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon's mutual information, as in models of rational inattention; but our theory differs from that of Sims (2003) in not assuming costless memory of past cognitive states. We show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that average beliefs will also differ from rational-expectations beliefs, with a bias that fluctuates forever with a variance that does not fall to zero even in the long run; and that more recent news will be given disproportionate weight in forecasts. We solve the model under a variety of assumptions about the degree of persistence of the variable to be forecasted and the horizon over which it must be forecasted, and examine how the nature of forecast biases depends on these parameters. The model provides a simple explanation for a number of features of reported expectations in laboratory and field settings, notably the evidence of over-reaction in elicited forecasts documented by Afrouzi et al. (2020) and Bordalo et al. (2020a).
    Keywords: over-reaction; rational inattention; Survey expectations
    JEL: D84 E03 G41
    Date: 2020–11
  13. By: Müller, Daniel; Schmitz, Patrick W.
    Abstract: A principal hires an agent to provide a verifiable service. Initially, the agent can exert unobservable effort to reduce his disutility from providing the service. If the agent is free to waive his right to quit, he may voluntarily sign a contract specifying an inefficiently large service level, while there are insufficient incentives to exert effort. If the agent's right to quit is inalienable, the underprovision of effort may be further aggravated, but the service level is ex post efficient. Overall, it turns out that the total surplus can be larger when agents are not permitted to contractually waive their right to quit work. Yet, we also study an extension of our model in which even the agent can be strictly better off when the parties have the contractual freedom to waive the agent's right to quit.
    Keywords: efficiency wages; Incentive theory; Labor contracts; law and economics; moral hazard
    JEL: D23 D86 J83 K12 K31
    Date: 2020–12
  14. By: Rahul Deb; Ludovic Renou
    Abstract: A researcher observes a finite sequence of choices made by multiple agents in a binary-state environment. Agents maximize expected utilities that depend on their chosen alternative and the unknown underlying state. Agents learn about the time-varying state from the same information and their actions change because of the evolving common belief. The researcher does not observe agents' preferences, the prior, the common information and the stochastic process for the state. We characterize the set of choices that are rationalized by this model and generalize the information environments to allow for private information. We discuss the implications of our results for uncovering discrimination and committee decision making.
    Date: 2021–05
  15. By: Michele Crescenzi
    Abstract: We study how a consensus emerges in a finite population of like-minded individuals who are asymmetrically informed about the realization of the true state of the world. Agents observe a private signal about the state and then start exchanging messages. Generalizing the classical model of rational dialogues of Geanakoplos and Polemarchakis (1982) and its subsequent extensions, we dispense with the standard assumption that the state space is a probability space and we do not put any bound on the cardinality of the state space itself or the information partitions. We show that a class of rational dialogues can be found that always lead to consensus provided that three main conditions are met. First, everybody must be able to send messages to everybody else, either directly or indirectly. Second, communication must be reciprocal. Finally, agents need to have the opportunity to engage in dialogues of transfinite length.
    Date: 2021–05
  16. By: Inés Macho-Stadler (UAB - Universitat Autònoma de Barcelona); David Pérez-Castrillo (UAB - Universitat Autònoma de Barcelona); Nicolas Quérou (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: We consider a market where "standard" risk-neutral agents coexist with "goaloriented" agents who, in addition to the expected income, seek a high-enough monetary payoff (the "trigger") to fulfill a goal. We analyze a two-sided one-to-one matching model where the matching between principals and agents and incentive contracts are endogenous. In any equilibrium contract, goal-oriented agents are matched with the principals with best projects and receive the trigger with positive probability. Moreover, goal and monetary incentives are complementary: goaloriented agents receive stronger monetary incentives. Finally, we discuss policy interventions in relevant environments.
    Keywords: Goal-oriented agents,incentives,matching market
    Date: 2021–06
  17. By: Urgun, Can; Yariv, Leeat
    Abstract: We study a model of retrospective search in which an agent-a researcher, an online shopper, or a politician-tracks the value of a product. Discoveries beget discoveries and their observations are correlated over time, which we model using a Brownian motion. The agent decides both how ambitiously, or broadly, to search, and for how long. We fully characterize the optimal search policy and show that it entails constant scope of search and a simple stopping boundary. We also show the special features that emerge from contracting with a retrospective searcher.
    Keywords: Contracting; Drawdown Stopping Boundary; Retrospective Search
    JEL: C61 C73 D83
    Date: 2020–12
  18. By: Pycia, Marek; Woodward, Kyle
    Abstract: The pay-as-bid (or discriminatory) auction is a prominent format for selling homogenous goods such as treasury securities and commodities. We prove the uniqueness of its pure-strategy Bayesian Nash equilibrium and establish a tractable representation of equilibrium bids. Building on these results we analyze the optimal design of pay-as-bid auctions, as well as uniform-price auctions (the main alternative auction format), allowing for asymmetric information. We show that supply transparency and full disclosure are optimal in pay-as-bid, though not necessarily in uniform-price; pay-as-bid is revenue dominant and might be welfare dominant; and, under assumptions commonly imposed in empirical work, the two formats are revenue and welfare equivalent.
    Date: 2021–01
  19. By: Víctor González-Jiménez
    Abstract: I show that stochastic contracts are powerful motivational devices when agents distort probabilities. Stochastic contracts allow the principal to target probabilities that, when distorted by the agent, enhance the agent's motivation to exert effort on the delegated task. This novel source of incentives is absent in traditional contracts. A theoretical framework and an experiment demonstrate that stochastic contracts targeting small probabilities, and thus exposing the agent to a large degree of risk, generate higher performance levels than traditional contracting modalities. A result that contradicts the standard rationale that optimal contracts should feature a tradeoff between insurance and efficiency. This unintuitive finding is attributed to probability distortions caused by likelihood insensitivity - cognitive limitations that restrict the accurate evaluation of probabilities.
    JEL: C91 C92 J16 J24
    Date: 2101–05
  20. By: Wanchang Zhang
    Abstract: We study the design of revenue-maximizing bilateral trade mechanisms in the correlated private value environment. We assume the designer only knows the expectations of the agents' values, but knows neither the marginal distribution nor the correlation structure. The performance of a mechanism is evaluated in the worst-case over the uncertainty of joint distributions that are consistent with the known expectations. Among all dominant-strategy incentive compatible and ex-post individually rational mechanisms, we provide a complete characterization of the maxmin trade mechanisms and the worst-case joint distributions.
    Date: 2021–05
  21. By: Bardhi, Arjada; Bobkova, Nina
    Abstract: We study optimal minipublic design with endogenous evidence. A policymaker selects a group of citizens-a minipublic-for advice on the desirability of a policy. Citizens can discover local evidence but might be deterred by uncertainty about the policymaker's adoption standard. We show that such uncertainty can be detrimental to evidence discovery even with costless evidence, civic-minded citizens, and ex ante aligned players. Evidence discovery is hardest to sustain under moderate uncertainty. The optimal minipublic has low diversity: it overrepresents citizens around the median citizen and underrepresents those at the margins. Our findings bear implications for the French Citizens' Convention on Climate.
    Keywords: demographic diversity; evidence discovery; informational diversity; minipublic; Political uncertainty
    JEL: D71 D72 D83
    Date: 2021–01
  22. By: Nocke, Volker; Strausz, Roland
    Abstract: We develop a theory of collective brand reputation for markets in which product quality is jointly determined by local and global players. In a repeated game of imperfect public monitoring, we model collective branding as a pooling of quality signals generated in different markets. Such pooling yields a beneficial informativeness effect for the actions of a global player present in all markets, but also harmful free-riding by local, market-specific players. The resulting tradeoff yields a theory of optimal brand size and revenue sharing, applying to platform markets, franchising, licensing, umbrella branding, and firms with team production.
    Keywords: Collective branding; free riding; Imperfect Monitoring; repeated games; reputation
    Date: 2021–01
  23. By: Hitoshi Matsushima (University of Tokyo)
    Abstract: This study investigates an axiomatic approach to in-kind assignment problems with single-unit demand. We consider multiple ethical criteria regarding which agents should be assigned that conflict with each other. To make compromises between criteria, we introduce two methods for configuring social choice rules that map from various problems to agents who are assigned slots: the method of procedure and the method of aggregation. From inter-problem regularities, we demonstrate characterization results, implying that the method of procedure emphasizes consistent respect for individual criteria across problems, while the method of aggregation emphasizes consistent respect for individual agents across problems. These methods are incompatible because only ethical dictatorships are induced by both methods at the same time. We show that the method of aggregation is superior when we can utilize detailed information about ethical concerns such as cardinality and comparability, while the method of procedure is superior when there are severe informational limitations.
    Date: 2021–05
  24. By: Naomi Moy; Ho Fai Chan; Frank Mathmann; Markus Schaffner; Benno Torgler
    Abstract: Self-confidence has long been regarded as one of the key qualities in determining entrepreneurial success. In markets with uncertainty, like crowdfunding, entrepreneurial confidence is an important signal that lowers the information imbalance for potential investors. However, current literature on confidence is limited in three ways; first is the limited understanding of confidence in interpersonal interactions; second is the accurate measurement of confidence and thirdly, limited insight on whether an optimal level of confidence exists. We use two novel behavioral approaches to measure self and exhibited confidence and examine their relation to entrepreneurial success in reward-based crowdfunding. Derived from ex-ante information (i.e., before realization of success), our measurements for confidence allow us to draw causal inferences, allowing for contributions to confidence and displays of interpersonal emotion literature. By analyzing over 70,000 Kickstarter projects, we show an optimal level of entrepreneurial confidence exists in determining funding received, popularity, and likelihood of success.
    Keywords: Behavioral; crowdfunding; entrepreneur; exhibiting confidence; interpersonal confidence
    Date: 2021–05
  25. By: Bar-Isaac, Heski; Caruana, Guillermo; Cuñat, Vicente
    Abstract: We present a model of product design. In our framework, there is an inherent trade-off associated with choosing between broad or niche designs. More-targeted designs are able to excite specific types of consumers, but at the cost of alienating others. We adapt the familiar Salop (1979) circle by allowing firms to locate on the interior. In contrast to previous research that exogenously assumed extreme designs, we provide conditions that ensure extreme or intermediate designs in monopoly, monopolistic competition, and duopoly. We use the framework to qualify earlier findings in the literature and support the robustness of others.
    JEL: D42 D43 M31
    Date: 2021–01
  26. By: Mauring, Eeva
    Abstract: I study limited price discrimination based on search costs. "Shoppers" have a zero and "nonshoppers" a positive search cost. A consumer faces a nondiscriminatory "common" price with some probability, or a discriminatory price. In equilibrium, firms mix over the common and the shoppers' discriminatory prices, but set a singleton nonshoppers' discriminatory price. Less likely price discrimination mostly benefits consumers. An individual firm's profit can increase in the number of firms. These results have important implications for regulations that limit price discrimination via reduced tracking (e.g., EU's GDPR, California's CCPA) and for evaluating competition online based on the number of firms.
    Keywords: consumer tracking; cookies; GDPR; Imperfect Competition; Online markets; price discrimination; sequential search
    JEL: D43 D83
    Date: 2021–01
  27. By: Calzolari, Giacomo; Denicolò, Vincenzo
    Abstract: Contracts that reference rivals' volumes (RRV contracts), such as exclusive dealing or market-share rebates, have been a long-standing concern in antitrust because of their possible exclusionary effects. We show, however, that it is more profitable to use these contracts to exploit rivals rather than to foreclose them. By optimally designing RRV contracts, a dominant firm may, indeed, obtain higher profits than if it were an unchallenged monopolist. In the most favorable cases, it can earn as much as if it could eliminate the competition and acquire the rivals' specific technological capabilities free of charge.
    Keywords: Exclusive dealing; Exploitation; foreclosure; Market-share discounts
    JEL: D42 D82 L42
    Date: 2020–12
  28. By: Calvano, Emilio; Calzolari, Giacomo; Denicolò, Vincenzo; Pastorello, Sergio
    Abstract: We show that if they are allowed enough time to complete the learning, Q-learning algorithms can learn to collude in an environment with imperfect monitoring adapted from Green and Porter (1984), without having been instructed to do so, and without communicating with one another. Collusion is sustained by punishments that take the form of "price wars" triggered by the observation of low prices. The punishments have a finite duration, being harsher initially and then gradually fading away. Such punishments are triggered both by deviations and by adverse demand shocks.
    Keywords: artificial intelligence; Collusion; Imperfect Monitoring; Q-Learning
    JEL: D43 D83 L13 L41
    Date: 2021–01

This nep-mic issue is ©2021 by Jing-Yuan Chiou. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
General information on the NEP project can be found at For comments please write to the director of NEP, Marco Novarese at <>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.