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on Microeconomics |
| By: | Salvador Barberà; Anke Gerber |
| Abstract: | We formalize, under the name of games of addition, the strategic inter- action between agents that can play non-simultaneously by adding payoff relevant actions to those that any other players or themselves have already taken previously, but may also agree unanimously to stop adding them and collect the payoffs associated with the truncated sequence of moves. Our formalization differs from that of extensive form games in that the order of the agents’ moves is not predetermined but emerges endogenously when applying an adapted version of a solution concept proposed by Dutta, Jackson and Le Breton (2004). We provide results regarding the properties of solutions to games of addition, and we also compare their corresponding equilibria with those we would obtain if using extensive form games and subgame perfection as alternative tools of analysis. |
| Keywords: | sequential games, order of play |
| JEL: | C72 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1443&r= |
| By: | Marco Battaglini; Thomas R. Palfrey |
| Abstract: | Collective action is a dynamic process where individuals in a group assess over time the benefits and costs of participating toward the success of a collective goal. Early participation improves the expectation of success and thus stimulates the subsequent participation of other individuals who might otherwise be unwilling to engage. On the other hand, a slow start can depress expectations and lead to failure for the group. Individuals have an incentive to procrastinate, not only in the hope of free riding, but also in order to observe the flow of participation by others, which allows them to better gauge whether their own participation will be useful or simply wasted. How do these phenomena affect the probability of success for a group? As the size of the group increases, will a “power of large numbers” prevail producing successful outcomes, or will a “curse of large numbers” lead to failure? In this paper, we address these questions by studying a dynamic collective action problem in which n individuals can achieve a collective goal if a share of them takes a costly action (e.g., participate in a protest, join a picket line, or sign an environmental agreement). Individuals have privately known participation costs and decide over time if and when to participate. We characterize the equilibria of this game and show that under general conditions the eventual success of collective action is necessarily probabilistic. The process starts for sure, and hence there is always a positive probability of success; however, the process “gets stuck” with positive probability, in the sense that participation stops short of the goal. Equilibrium outcomes have a simple characterization in large populations: welfare converges to either full efficiency or zero as n→∞ depending on a precise condition on the rate at which the share required for success converges to zero. Whether success is achievable or not, delays are always irrelevant: in the limit, success is achieved either instantly or never. |
| JEL: | D71 D74 D82 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32473&r= |
| By: | Swagata Bhattacharjee (Ashoka University); Srijita Ghosh (Ashoka University); Suraj Shekhar (Ashoka University) |
| Abstract: | We consider a static cheap talk model in an environment with either one or two experts whose biases are privately known by the experts themselves. Before the experts learn the state, they send a cheap talk message about their bias to the decision maker. Subsequently, the decision maker chooses one expert to get state relevant advice from. We ask two questions - One, is there an equilibrium where the experts’ bias is fully revealed? Two, is the bias revealing equilibrium welfare improving for the decision maker? We find that when there is only one expert, there is no bias revealing equilibrium. However, if there are two experts, there exists a bias revealing equilibrium, and under some conditions it gives the decision maker more utility than any equilibrium which is possible without bias revelation. This highlights a new channel through which sender competition can benefit the decision maker, through which sender competition can benefit the decision maker. |
| Keywords: | bias revelation; Cheap talk; multiple senders; uncertain bias |
| Date: | 2024–01–29 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:109&r= |
| By: | Yuya Wakabayashi (JSPS Research Fellow (DC2), Graduate School of Economics, Osaka University) |
| Abstract: | We examine a simple hidden information economy with a single agent, multiple identical firms, and two goods. The agent’s states are unknown to the firms. The game unfolds in two stages: in the first stage, firms offer a menu of allocations, and in the second stage, the agent selects her preferred allocation from the offered allocations. We show that, in almost all cases, the constrained efficient allocation cannot be implemented by a subgame perfect equilibrium in the game. |
| Keywords: | Asymmetric information, Constrained efficiency, Nash implementation |
| JEL: | D47 D82 D86 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:osp:wpaper:24e002&r= |
| By: | Mihir Bhattacharya (Ashoka University); Ojasvi Khare (Indian Statistical Institute) |
| Abstract: | We consider a social choice model where voters have single-peaked preferences over the alternatives that are aggregated to produce contiguous sets or intervals of fixed cardinality, L. This is applicable in situations where the alternatives can be arranged in a line (e.g. plots of land) and a contiguous subset of these is required (e.g. a hospital or a school). We define interval-social choice correspondences (I-SCCs) on profiles of single-peaked preferences which select intervals. We extend single-peaked preferences to intervals using responsiveness. We show that generalized median-interval (GMI) rules are the only strategy-proof, anonymous and interval efficient I-SCCs. These rules are interval versions of generalized median voter rules which consist of the median, min and max rules. We show that responsiveness over intervals is necessary for the strategy-proofness of the GMI rule if preferences over alternatives are single-peaked. |
| Keywords: | median voter; responsive; single-peaked preferences; social choice correspondence; strategy-proofness; voter |
| Date: | 2023–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:89&r= |
| By: | Galit Ashkenazi-Golan; Dominik Karos; Ehud Lehrer |
| Abstract: | A decision maker repeatedly chooses one of a finite set of actions. In each period, the decision maker's payoff depends on fixed basic payoff of the chosen action and the frequency with which the action has been chosen in the past. We analyze optimal strategies associated with three types of evaluations of infinite payoffs: discounted present value, the limit inferior, and the limit superior of the partial averages. We show that when the first two are the evaluation schemes, a stationary strategy can always achieve the best possible outcome. However, for the latter evaluation scheme, a stationary strategy can achieve the best outcome only if all actions that are chosen with strictly positive frequency by an optimal stationary strategy have the same basic payoff. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.00561&r= |
| By: | Konstantin von Beringe; Mark Whitmeyer |
| Abstract: | In order to study updating rules, we consider the problem of a malevolent principal screening an imperfectly Bayesian agent. We uncover a fundamental dichotomy between underreaction and overreaction to information. If an agent's posterior is farther away from the prior than it should be under Bayes' law, she can always be exploited by the principal to an unfettered degree: the agent's ex ante expected loss can be made arbitrarily large. In stark contrast, an agent who underreacts (whose posterior is closer to the prior than the Bayesian posterior) cannot be exploited at all. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.08087&r= |
| By: | Sebastian Schweighofer-Kodritsch (HU Berlin); Roland Strausz (HU Berlin) |
| Abstract: | We cast mechanism design with evidence in the framework of Myerson (1982), whereby his generalized revelation principle directly applies and yields standard notions of incentive compatible direct mechanisms. Their specific nature depends on whether the agent's (verifiable) presentation of evidence is contractually controllable, however. For deterministic implementation, we show that, in general, such control has value, and we offer two independent conditions under which this value vanishes, one on evidence (WET) and another on preferences (TIWO). Allowing for fully stochastic mechanisms, we also show how randomization generally has value and clarify to what extent this value vanishes under the common assumption of evidentiary normality (NOR). While, in general, the value of control extends to stochastic implementation, neither control nor randomization have any value if NOR holds together with WET or TIWO. |
| Keywords: | mechanism design; revelation principle; evidence; verifiable information; value of control; value of randomization; |
| JEL: | D82 |
| Date: | 2024–05–16 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:504&r= |
| By: | Yifan Zhang |
| Abstract: | Political and advertising campaigns increasingly exploit social networks to spread information and persuade people. This paper studies a persuasion model to examine whether such a strategy is better than simply sending public signals. Receivers in the model have heterogeneous priors and will pass on a signal if they are persuaded by it. I show that a risk neutral or risk loving sender prefers to use public signals, unless more sceptical receivers are sufficiently more connected in the social network. A risk averse sender may prefer to exploit the network. These results still hold when networks exhibit homophily. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.18965&r= |
| By: | Nicole Immorlica; Nicholas Wu; Brendan Lucier |
| Abstract: | We study the problem of a principal who wants to influence an agent's observable action, subject to an ex-post budget. The agent has a private type determining their cost function. This paper endogenizes the value of the resource driving incentives, which holds no inherent value but is restricted by finite availability. We characterize the optimal mechanism, showing the emergence of a pooling region where the budget constraint binds for low-cost types. We then introduce a linear value for the transferable resource; as the principal's value increases, the mechanism demands more from agents with binding budget constraint but less from others. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.15531&r= |
| By: | Christopher P. Chambers; Federico Echenique; Takashi Hayashi |
| Abstract: | This paper studies manipulation of belief aggregation rules in the setting where the society first collects individual's probabilistic opinions and then solves a public portfolio choice problem with common utility based on the aggregate belief. First, we show that belief reporting in Nash equilibrium under the linear opinion pool and log utility is identified as the profile of state-contingent wealth shares in parimutuel equilibrium with risk-neutral preference. Then we characterize belief aggregation rules which are Nash-implementable. We provide a necessary and essentially sufficient condition for implementability, which is independent of the common risk attitude. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.01655&r= |
| By: | Shuige Liu |
| Abstract: | We use a uniform framework to cognitive hierarchy (CH) solution concepts a decision-theoretical foundation by the epistemic game theoretical solution concept $\Delta$-rationalizability (Battigalli and Siniscalchi, 2003). We formulate level-$k$ strategic sophistication as an information type, and, by putting intuitive conditions on the the belief of players with a strategic sophistication, we define a restriction $\Delta^\kappa$, from which the levels of reasoning is endogenously determined. We show that in static games, Camerer, Ho, and Chong's (2004) CH solution generically coincides with the behavioral consequence of rationality, common belief in rationality, and transparency of $\Delta^\kappa$; based on this, we connect CH with Bayesian equilibrium. By adapting $\Delta^\kappa$ into dynamic games, we show that Lin and Palfrey's (2024) DCH solution generically coincides with the behavioral consequence of rationality, common strong belief in rationality, and transparency of (dynamic) $\Delta^\kappa$. The same structure could analyze many variations of CH in the literature. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.19623&r= |
| By: | Yuya Wakabayashi (JSPS Research Fellow (DC2), Graduate School of Economics, Osaka University); Ryosuke Sakai (School of Engineering, Tokyo Institute of Technology); Hiroki Shinozaki (Hitotsubashi Institute for Advanced Study, Hitotsubahi University) |
| Abstract: | We consider the single-object allocation problem with monetary transfers. Agents have hard budgets and their utility functions may exhibit income effects. We characterize truncated Vickrey rules with endogenous reserve prices by constrained efficiency or weak envy-freeness for equals, in addition to individual rationality, no subsidy for losers, and strategy-proofness. The same characterization result hold even if we replace weak envy freeness for equals with other fairness conditions; equal treatment of equals, envy-freeness, and anonymity in welfare. |
| Keywords: | Single-object allocation problem, Non-quasi-linear preference, Hard budget constraint, Efficiency, Fairness, Strategy-proofness, Vickrey rule with reserve prices |
| JEL: | D47 D63 D82 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:osp:wpaper:24e003&r= |
| By: | Salvador Barberà; Danilo Coelho |
| Abstract: | We propose mechanisms for two parties with potentially conflicting objectives to jointly select a predetermined number of candidates to occupy decision-making positions. Two leading examples of these situations are: i) the selection of an arbitrator panel by two conflicting firms, and ii) the bipartisan coalition's selection of a set of judges to occupy court vacancies. We analyze the efficiency, fairness, and simplicity of equilibrium outcomes in strategic games induced by these mechanisms. Their effectiveness hinges on the parties' preferences over the sets containing the required number of the candidates to be chosen. |
| Keywords: | appointing arbitrators, appointing judges, rule of k name, split appointment rules, compromise, unanimity compromise set, top compromise set |
| JEL: | D02 D71 D72 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1442&r= |
| By: | Tsuyoshi Toshimitsu (School of Economics, Kwansei Gakuin University) |
| Abstract: | Compatibility and connectivity are essential elements in a network economy. Using the degree of network compatibility as a measure of market competitiveness, we consider the impact of compatibility on profit incentives to innovate in a network goods industry. That is, an increase in the degree of network compatibility possibly reduces market competitive pressure. In addition, we investigate the impact on consumer benefits (i.e., marginal consumer surplus) caused by the innovation. We demonstrate that as the degree of compatibility increases, the profit incentives to innovate first decrease, then increase (i.e., a U-shaped function of compatibility); but, conversely, the consumer benefits first increase, then decrease (i.e., an inverted U-shaped function of compatibility). |
| Keywords: | innovation; network compatibility; a fulfilled expectation; cost-reducing R&D; Cournot duopoly |
| JEL: | D43 L13 L15 O31 |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:kgu:wpaper:274&r= |
| By: | Zongxia Liang; Yi Xia; Bin Zou |
| Abstract: | We introduce a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle; the reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus; the competition game between the two reinsurers is settled by a non-cooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semi-closed form. Additionally, we obtain interesting sensitivity results for the equilibrium strategies through both an analytical and numerical study. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.06235&r= |
| By: | Chung-Han Hsieh; Yi-Shan Wong |
| Abstract: | This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which are deterministic and others are stochastic. The decision-maker's cumulative value is updated at each stage, reflecting the outcomes of the chosen alternatives. After formulating this as a stochastic control problem, we delineate the necessary optimality conditions for it. Two illustrative examples from optimal betting and inventory management are provided to support our theory. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.13371&r= |
| By: | Alessandro Lizzeri; Eran Shmaya; Leeat Yariv |
| Abstract: | Starting from Robbins (1952), the literature on experimentation via multi-armed bandits has wed exploration and exploitation. Nonetheless, in many applications, agents' exploration and exploitation need not be intertwined: a policymaker may assess new policies different than the status quo; an investor may evaluate projects outside her portfolio. We characterize the optimal experimentation policy when exploration and exploitation are disentangled in the case of Poisson bandits, allowing for general news structures. The optimal policy features complete learning asymptotically, exhibits lots of persistence, but cannot be identified by an index a la Gittins. Disentanglement is particularly valuable for intermediate parameter values. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.19116&r= |
| By: | Francis Bloch (Universite´ Paris 1 and Paris School of Economics); Bhaskar Dutta (Ashoka University); Marcin Dziubi´nski (Institute of Informatics, University of Warsaw) |
| Abstract: | We propose and study a model of strategic network design and exploration where the hider, subject to a budget constraint restricting the number of links, chooses a connected network and the location of an object. Meanwhile, the seeker, not observing the network and the location of the object, chooses a network exploration strategy starting at a fixed node in the network. The network exploration follows the expanding search paradigm of Alpern and Lidbetter (2013). We obtain a Nash equilibrium and characterize equilibrium payoffs in the case of linking budget allowing for trees only. We also give an upper bound on the expected number of steps needed to find the hider for the case where the linking budget allows for at most one cycle in the network. |
| Keywords: | Network exploration; networks; Strategic hiding |
| Date: | 2024–04–12 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:112&r= |
| By: | Tomasz Strzalecki |
| Abstract: | I show how variational Bayes can be used as a microfoundation for a popular model of non-Bayesian updating. All the results here are mathematically trivial, but I think this direction is potentially interesting. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.08796&r= |