nep-mic New Economics Papers
on Microeconomics
Issue of 2023‒11‒13
fifteen papers chosen by
Jing-Yuan Chiou, National Taipei University

  1. Belief formation and the persistence of biased beliefs By Olivier Compte
  2. Managing Persuasion Robustly: The Optimality of Quota Rules By Dirk Bergemann; Tan Gan; Yingkai Li
  3. Information Design in Cheap Talk By Qianjun Lyu; Wing Suen
  4. Markovian persuasion with two states By Ashkenazi-Golan, Galit; Hernández, Penélope; Neeman, Zvika; Solan, Eilon
  5. Pecuniary Emulation and Invidious Distinction: Signaling under Behavioral Diversity By Junichiro Ishida; Wing Suen
  6. Best-Response Dynamics in Tullock Contests with Convex Costs By Abheek Ghosh
  7. Forecasts as Repeated Cheap Talk from an Expert of Unknown Statistical Bias By Valsecchi, Irene
  8. Reference-dependent choice bracketing By Pauline Vorjohann
  9. Mechanism Design for Large Language Models By Paul Duetting; Vahab Mirrokni; Renato Paes Leme; Haifeng Xu; Song Zuo
  10. Cheap Talking Algorithms By Daniele Condorelli; Massimiliano Furlan
  11. Substitutes markets with budget constraints: solving for competitive and optimal prices By Simon Finster; Paul Goldberg; Edwin Lock
  12. A new proof for the existence of Nash equilibrium By Davide Carpentiere; Stephen Watson
  13. Non-Price Strategies of Marketplaces: A Survey By Belleflamme, Paul; Johnen, Johannes
  14. Modeling social norms: an integration of the norm-utility approach with beliefs dynamics By Gavrilets, Sergey; Tverskoi, Denis; Sánchez, Angel
  15. Separately Convex and Separately Continuous Preferences: On Results of Schmeidler, Shafer, and Bergstrom-Parks-Rader By Metin Uyanik; Aniruddha Ghosh; M. Ali Khan

  1. By: Olivier Compte
    Abstract: We propose a belief-formation model where agents attempt to discriminate between two theories, and where the asymmetry in strength between confirming and disconfirming evidence tilts beliefs in favor of theories that generate strong (and possibly rare) confirming evidence and weak (and frequent) disconfirming evidence. In our model, limitations on information processing provide incentives to censor weak evidence, with the consequence that for some discrimination problems, evidence may become mostly one-sided, independently of the true underlying theory. Sophisticated agents who know the characteristics of the censored data-generating process are not lured by this accumulation of ``evidence'', but less sophisticated ones end up with biased beliefs.
    Date: 2023–10
  2. By: Dirk Bergemann (Yale University); Tan Gan (Yale University); Yingkai Li (Yale University)
    Abstract: We study a sender-receiver model where the receiver can commit to a decision rule before the sender determines the information policy. The decision rule can depend on the signal structure and the signal realization that the sender adopts. This framework captures applications where a decision-maker (the receiver) solicit advice from an interested party (sender). In these applications, the receiver faces uncertainty regarding the senderÕs preferences and the set of feasible signal structures. Consequently, we adopt a unified robust analysis framework that includes max-min utility, min-max regret, and min-max approximation ratio as special cases. We show that it is optimal for the receiver to sacrifice ex-post optimality to perfectly align the senderÕs incentive. The optimal decision rule is a quota rule, i.e., the decision rule maximizes the receiverÕs ex-ante payoff subject to the constraint that the marginal distribution over actions adheres to a consistent quota, regardless of the senderÕs chosen signal structure.
    Date: 2023–10–19
  3. By: Qianjun Lyu; Wing Suen
    Abstract: An uninformed sender publicly commits to an informative experiment about an uncertain state, privately observes its outcome, and sends a cheap-talk message to a receiver. We provide an algorithm valid for arbitrary state-dependent preferences that will determine the sender’s optimal experiment and his equilibrium payoff under binary state space. We give sufficient conditions for information design to be valuable or not under different payoff structures. These conditions depend more on marginal incentives - how payoffs vary with the state - than on the alignment of sender’s and receiver’s rankings over actions within a state. The algorithm can be easily modified to study canonical cheap talk games with a perfectly informed sender.
    Keywords: marginal incentives, common interest, concave envelope, quasiconcave envelope, double randomization
    JEL: D82 D83
    Date: 2023–10
  4. By: Ashkenazi-Golan, Galit; Hernández, Penélope; Neeman, Zvika; Solan, Eilon
    Abstract: This paper addresses the question of how to best communicate information over time in order to influence an agent's belief and induced actions in a model with a binary state of the world that evolves according to a Markov process, and with a finite number of actions. We characterize the sender's optimal message strategy in the limit, as the length of each period decreases to zero. We show that the limit optimal strategy is myopic for beliefs smaller than the invariant distribution of the underlying Markov process. For beliefs larger than the invariant distribution, the optimal policy is more elaborate and involves both silence and splitting of the receiver's beliefs; it is not myopic.
    Keywords: Bayesian persuasion; information design; Markov games; repeated games with incomplete information; 2510/17; Elsevier deal
    JEL: D82 D83
    Date: 2023–11–01
  5. By: Junichiro Ishida; Wing Suen
    Abstract: We introduce behavioral diversity to an otherwise standard signaling model, in which a fraction of agents choose their signaling actions according to an exogenous distribution. These behavioral agents provide opportunities for strategic low-type agents to successfully emulate higher types in equilibrium, which in turn reduces the cost for strategic high-type agents to separate from lower types. Behavioral diversity thus improves the equilibrium payoffs to all types of strategic agents. The model also exhibits a convergence property which is intuitively more appealing than the least-cost separating equilibrium of the standard setting.
    Date: 2023–10
  6. By: Abheek Ghosh
    Abstract: We study the convergence of best-response dynamics in Tullock contests with convex cost functions (these games always have a unique pure-strategy Nash equilibrium). We show that best-response dynamics rapidly converges to the equilibrium for homogeneous agents. For two homogeneous agents, we show convergence to an $\epsilon$-approximate equilibrium in $\Theta(\log\log(1/\epsilon))$ steps. For $n \ge 3$ agents, the dynamics is not unique because at each step $n-1 \ge 2$ agents can make non-trivial moves. We consider the model proposed by \cite{ghosh2023best}, where the agent making the move is randomly selected at each time step. We show convergence to an $\epsilon$-approximate equilibrium in $O(\beta \log(n/(\epsilon\delta)))$ steps with probability $1-\delta$, where $\beta$ is a parameter of the agent selection process, e.g., $\beta = n^2 \log(n)$ if agents are selected uniformly at random at each time step. We complement this result with a lower bound of $\Omega(n + \log(1/\epsilon)/\log(n))$ applicable for any agent selection process.
    Date: 2023–10
  7. By: Valsecchi, Irene
    Abstract: For two periods an expert E announces his forecast of the state to a decision-maker D who chooses action. They disagree about the precision of the probability assessments. At the end of period 1 the state is observed. In the last period E makes announcements more extreme than his forecasts. Despite countable equilibria, full revelation is never realised. When in period 1 E is interested in reputation only, the initial equilibrium partition is finite; E makes announcements of greater uncertainty with respect to his forecasts. When E is interested in action too, reputational concerns mitigate exaggerated reports.
    Keywords: Research Methods/ Statistical Methods
    Date: 2023–10–26
  8. By: Pauline Vorjohann (Department of Economics, University of Exeter)
    Abstract: I derive a theoretical model of choice bracketing from two behavioral axioms in an expected utility framework. The first behavioral axiom establishes a direct link between narrow bracketing and correlation neglect. The second behavioral axiom identifies the reference point as the place where broad and narrow preferences are connected. In my model, the narrow bracketer is characterized by an inability to process changes from the reference point in different dimensions simultaneously. As a result, her tradeoffs between dimensions are distorted. While she disregards interactions between actual outcomes, she appreciates these interactions mistakenly with respect to the reference point.
    Keywords: narrow bracketing, correlation neglect, reference dependence, axiomatic foundation
    JEL: D3 D11 D91
    Date: 2023–09–05
  9. By: Paul Duetting; Vahab Mirrokni; Renato Paes Leme; Haifeng Xu; Song Zuo
    Abstract: We investigate auction mechanisms to support the emerging format of AI-generated content. We in particular study how to aggregate several LLMs in an incentive compatible manner. In this problem, the preferences of each agent over stochastically generated contents are described/encoded as an LLM. A key motivation is to design an auction format for AI-generated ad creatives to combine inputs from different advertisers. We argue that this problem, while generally falling under the umbrella of mechanism design, has several unique features. We propose a general formalism -- the token auction model -- for studying this problem. A key feature of this model is that it acts on a token-by-token basis and lets LLM agents influence generated contents through single dimensional bids. We first explore a robust auction design approach, in which all we assume is that agent preferences entail partial orders over outcome distributions. We formulate two natural incentive properties, and show that these are equivalent to a monotonicity condition on distribution aggregation. We also show that for such aggregation functions, it is possible to design a second-price auction, despite the absence of bidder valuation functions. We then move to designing concrete aggregation functions by focusing on specific valuation forms based on KL-divergence, a commonly used loss function in LLM. The welfare-maximizing aggregation rules turn out to be the weighted (log-space) convex combination of the target distributions from all participants. We conclude with experimental results in support of the token auction formulation.
    Date: 2023–10
  10. By: Daniele Condorelli; Massimiliano Furlan
    Abstract: We simulate behaviour of independent reinforcement learning algorithms playing the Crawford and Sobel (1982) game of strategic information transmission. We show that a sender and a receiver training together converge to strategies close to the exante optimal equilibrium of the game. Hence, communication takes place to the largest extent predicted by Nash equilibrium given the degree of conflict of interest between agents. The conclusion is shown to be robust to alternative specifications of the hyperparameters and of the game. We discuss implications for theories of equilibrium selection in information transmission games, for work on emerging communication among algorithms in computer science and for the economics of collusions in markets populated by artificially intelligent agents.
    Date: 2023–10
  11. By: Simon Finster; Paul Goldberg; Edwin Lock
    Abstract: Markets with multiple divisible goods have been studied widely from the perspective of revenue and welfare. In general, it is well known that envy-free revenue-maximal outcomes can result in lower welfare than competitive equilibrium outcomes. We study a market in which buyers have quasilinear utilities with linear substitutes valuations and budget constraints, and the seller must find prices and an envy-free allocation that maximise revenue or welfare. Our setup mirrors markets such as ad auctions and auctions for the exchange of financial assets. We prove that the unique competitive equilibrium prices are also envy-free revenue-maximal. This coincidence of maximal revenue and welfare is surprising and breaks down even when buyers have piecewise-linear valuations. We present a novel characterisation of the set of "feasible" prices at which demand does not exceed supply, show that this set has an elementwise minimal price vector, and demonstrate that these prices maximise revenue and welfare. The proof also implies an algorithm for finding this unique price vector.
    Date: 2023–10
  12. By: Davide Carpentiere; Stephen Watson
    Abstract: We present a new proof for the existence of a Nash equilibrium, which involves no fixed point theorem. The self-contained proof consists of two parts. The first part introduces the notions of root function and pre-equilibrium. The second part shows the existence of pre-equilibria and Nash equilibria.
    Date: 2023–10
  13. By: Belleflamme, Paul (Université catholique de Louvain, LIDAM/CORE, Belgium); Johnen, Johannes (Université catholique de Louvain, LIDAM/CORE, Belgium)
    Abstract: Two-sided platforms have a great impact on markets nowadays. Especially, online marketplaces design markets and choose many of the rules that govern how buyers and sellers interact. Researchers studied two-sided platforms very actively over the last two decades. We review the economic literature from two angles: we focus on marketplaces and we concentrate on non-price strategies that marketplaces employ to govern interactions (like user steering, self-preferencing, rating and review systems, data and targeting, privacy, and user protection).
    Keywords: Two-Sided Platforms ; Marketplaces ; Platform Governance ; Platform Strategy ; Platform Regulation ; Platform Self-Regulation
    Date: 2023–05–31
  14. By: Gavrilets, Sergey; Tverskoi, Denis; Sánchez, Angel
    Abstract: We review theoretical approaches for modeling the origin, persistence and change of social norms. The most comprehensive models describe the coevolution of behaviors, personal, descriptive, and injunctive norms while considering influences of various authorities and accounting for cognitive processes and between-individual differences. Models show that social norms can improve individual and group well-being. Under some conditions though deleterious norms can persist in the population through conformity, preference falsification, and pluralistic ignorance. Polarization in behavior and beliefs can be maintained, even when societal advantages of particular behaviors or belief systems over alternatives are clear. Attempts to change social norms can backfire through cognitive processes including cognitive dissonance and psychological reactance. Under some conditions social norms can change rapidly via tipping point dynamics. Norms can be highly susceptible to manipulation, and network structure influences their propagation. Future models should incorporate network structure more thoroughly, explicitly study online norms, consider cultural variations, and be applied to real-world processes.
    Date: 2023–10–19
  15. By: Metin Uyanik; Aniruddha Ghosh; M. Ali Khan
    Abstract: We provide necessary and sufficient conditions for a correspondence taking values in a finite-dimensional Euclidean space to be open so as to revisit the pioneering work of Schmeidler (1969), Shafer (1974), Shafer-Sonnenschein (1975) and Bergstrom-Rader-Parks (1976) to answer several questions they and their followers left open. We introduce the notion of separate convexity for a correspondence and use it to relate to classical notions of continuity while giving salience to the notion of separateness as in the interplay of separate continuity and separate convexity of binary relations. As such, we provide a consolidation of the convexity-continuity postulates from a broad inter-disciplinary perspective and comment on how the qualified notions proposed here have implications of substantive interest for choice theory.
    Date: 2023–09

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