Pooling Equilibrium Research Articles

The evolution of Horn's rule

Horn's rule says that messages can be kept ambiguous if only a single interpretation is plausible. Speakers only perform costly disambiguation to convey surprising information. This paper shows that, while non‐cooperative game theory cannot justify Horn's rule, evolutionary game theory can. In order to model the evolution of signalling, the pooling equilibrium needs to be one's starting point. But in such an equilibrium, the plausible interpretation is made, and the receiver is therefore already predisposed to interpret absence of a signal as referring to a plausible event. From there on, a marked signal referring to an implausible event can evolve. At the same time, the paper identifies an exception to Horn's rule. If giving a plausible interpretation for an implausible event is very costly, then in the pooling equilibrium the implausible interpretation is always made. In this exceptional case, only an inefficient separating equilibrium disobeying Horn's rule can evolve.

Financial Deepening and Economic Growth in EU3: Core in Shapley-Shubik Game and General Equilibrium Models

Impacts of financial deepening on economic growth are examined with conventional financial asset GDP ratios, Shapley-Shubik core and general equilibrium modelling. It focuses on simultaneity between them rather than one way causation as found in the traditional McKinnon-Shaw analyses. General equilibrium results approximate the allocations for market with incomplete information though separating rather than pooling equilibrium generates efficient market outcome in presence of asymmetric information, particularly when the financial system operates under imperfect competition.. Empirical evidences from Germany, France and UK show how enhanced financial liberalisations can contribute towards growth in the 21 st century.

Gradual cooperation in the existence of outside options

The paper shows that efficient cooperation processes exhibit gradualism when each player does not know the likelihood that the other player exercises a stochastically available outside option. Two players, asymmetrically informed on this likelihood, play an infinitely repeated prisoner’s dilemma game. Each player is either the high type with the high probability to obtain the outside option or the low type. As time proceeds with neither player exercising the outside option, each player puts more probability on the belief that his partner is the low type, enabling the players to raise cooperation levels in the efficient pooling equilibrium.

The Banking Firm: The Role of Signaling with Collaterals

In this paper we challenge basic results of signaling models. In our banking model each project of a borrower is described by a continuous density of outcomes. Different density functions are classified according to second stochastisch dominance. Combining these features we find that in a banking model collateral is no longer in a position to signal the degree of riskiness of the borrower to the lender. In most cases the equilibrium is a pooling equilibrium.

Implicit contracting with a (potentially) reliable agent

Implicit contracts—informal agreements tied to observable, but non-verifiable information—play an important role in economic life. In this paper, we model such contracting in a two-period model with an agent that may be reliable, i.e., that always sticks to a promise he has previously made. We derive three main results: First, we show that a decrease in the discount factor may lead to a switch from a pooling equilibrium, where unreliable types mimic the reliable ones, to a separating one. Second, we find that a pooling equilibrium may yield a relatively lower surplus, because it puts a downward pressure on the effort that can be implemented. Combining both these results, we finally show that a decrease in the discount factor may be welfare-enhancing.

On the Competition between Insurers with Superior Information

We reinvestigate the case in which insurers have superior information regarding consumer's risk types, as studied by Villeneuve (2005, European Economic Review 49, 321-340). While Villeneuve produces interesting results on insurance contracts, the diverse outcomes make it difficult to pinpoint main implications. We make slight changes to the conditions in the Villeneuve's model by considering that there are a large number of insurers to ensure the competitive market; and that, in an equilibrium, contracts are required to be optimal even if some consumers are allowed to visit not all insurers announcing the same menus. We demonstrate that no pooling equilibrium can exist and that a separating equilibrium exists if and only if the difference between loss probabilities of types is large (types are distant). In a separating equilibrium, low risks are fully insured with actuarially fair premium, while high risks are self-insured. Our results provide a refinement of Villeneuve (2005), which is analogous to the monopoly case. This paper clarifies that high risk consumers bear information costs when insurers have superior information, in contrast with standard adverse selection models.

How to Price Imperfect Certification

This paper analyzes markets in which consumers do not directly observe the quality of the products but form their expectations about the quality based on the outcome of voluntary imperfect certification. I analyze how the certification fee impacts the decisions of the producers to apply for a certificate and whether to supply goods of required quality. I find that there are both separating (only high quality producers apply and obtain the certificate) and pooling (both high and low-quality producers apply and obtain) equilibria. I show that the pooling equilibrium exists when the certification fee is low, while the separating equilibrium requires high certification fees. Since the pooling equilibrium is not welfare optimal, excessive competition between certifiers, which lowers the certification fee, is not beneficial. This result complements Strausz (2005) who shows that high certification fees are required to prevent the corruption of the certifier.

Information Contents of Call-Put Options Trading Value Ratio

This paper investigates the lead-lag relationship between the call-put options trading value ratio and the KOSPI 200 returns using Chen, Lung, and Tay (2005, 2006)’s model. We report the evidence conSistent with a pooling equilibrium or that informed trades are executed in both equity and options markets when using all options. That is, KOSPI 200 index options and KOSPI 200 are closely interrelated. However, in case of using the short-term or out-of-the-money options, call-put oPtions trading value ratio uni-directionally leads KOSPI 200 index returns. Also under the volatile market condition, the lead effect of call-put options trading value ratio to KOSPI 200 index returns becomes stronger.

Screening equilibria in experimental markets

We conduct an experimental test of a screening model of an insurance market with asymmetric information. We first conduct three sessions in which the proportion of high risk buyers is such that a separating equilibrium should exist. We then conduct three more sessions in which the only change we make is decreasing the proportion of high risks such that the equilibrium is now a pooling equilibrium. In both treatments, the observed behavior converges to the equilibrium prediction.

Bid ask spread in a competitive market with institutions and order size

Large orders, particularly from institutions, are quite common these days and hence there is interest to know if institutional trading has any bearing on the price effect associated with large trades. Recent empirical studies contradict earlier evidence of negative price effect on selling large blocks and find no price effect associated with large trades. Existing theoretical framework suggests a monotonic and increasing adverse price effect for large trades, where the motivation for a large trade is private information. We model a trading system where pure information, information-liquidity, and pure liquidity traders trade small and large sizes. The pure information traders strategically choose an order size. Institutions trade only large sizes because of their low execution costs for large trades; they are information-liquidity traders whose ability to use an information signal to determine their trades is subject to a binding liquidity constraint. We show that in such a market a separating equilibrium where trade size is informative does not exist and hence there is no price effect for large trades. Trade size may be revealing only if there is a buy sell asymmetry (large buy size is not equal to large sell size) or the corresponding price effect is asymmetric (price effect due to a large buy is not equal to that of a large sell). Further for a pooling equilibrium to exist, where trade size is not informative, the width of the market denoted by the ratio of order size (large size/small size) needs to be small, while the shallowness (inverse depth) of the market denoted by the ratio between pure information and institutional trades and the information signal needs to be stronger (higher). Our results on bid and ask prices and spread confirm recent empirical evidence on price effect of large and institutional trades found in the literature.

Optimal Contracts for Health Services in the Presence of Waiting Times and Asymmetric Information

Abstract This study presents a model of optimal contracting for health services in the presence of excess demand and waiting times. We assume that: i) hospitals differ in their demand for treatment; ii) potential demand is private information of the provider; iii) specialists can dump patients; iv) activity and waiting times are contractible. A separating equilibrium exists when it is optimal for the purchaser to contract more activity and longer waiting times to those hospitals with higher demand. Hospitals with low demand gain informational rents. A pooling equilibrium may also occur.

Working Orders in Limit-Order Markets and Floor Exchanges

Limit-order markets and floor exchanges are analyzed, assuming an informed trader and discretionary liquidity traders use market orders and can either submit block orders or work their demands as a series of small orders. By working their demands, large market-order traders pool with small traders. We show that every equilibrium on a floor exchange must involve at least partial pooling. Moreover, there is always a fully pooling (worked-order) equilibrium on a floor exchange that is equivalent to a block-order equilibrium in a limit-order Our results also apply to the NYSE's proposed hybrid market.

Working Orders in Limit Order Markets and Floor Exchanges

ABSTRACTWe analyze limit order markets and floor exchanges, assuming an informed trader and discretionary liquidity traders use market orders and can either submit block orders or work their demands as a series of small orders. By working their demands, large market order traders pool with small traders. We show that every equilibrium on a floor exchange must involve at least partial pooling. Moreover, there is always a fully pooling (worked order) equilibrium on a floor exchange that is equivalent to a block order equilibrium in a limit order market.

A choice of auction format in seller cheating: a signaling game analysis

In this paper, we examine which auction format, first-price or second-price, a seller will choose when he can profitably cheat in a second price auction by observing all bids by possible buyers and submitting a shill bid as pretending to be a buyer. We model this choice of auction format in seller cheating as a signaling game in which the buyers may regard the selection of a second price auction by the seller as a signal that he is a shill bidder. By introducing trembling-hand perfectness as a refinement of signaling equilibrium, we find two possible strictly perfect signaling equilibria. One is a separating equilibrium in which a noncheating honest seller selects a first price auction and a cheating seller does a second price auction. In another pooling equilibrium, however, both cheating and non-cheating sellers select a second price auction. The conclusion that a seller chooses a second price auction even if he cannot cheat is in contrast to the previous literature, which focused on the case of independent values.

Optimum commodity taxation in pooling equilibria

This paper extends the standard model of optimum commodity taxation (Ramsey, F., 1927. A Contribution to the Theory of Taxation. Economic Journal 37, 47–61; Diamond, P., Mirrlees, J., 1971. Optimal Taxation and Public Production, II: "Tax Rules". American Economic Review 61, 261–278) to a competitive economy in which markets are inefficient due to asymmetric information. Insurance markets are prime examples: consumers impose varying costs on suppliers but firms cannot associate costs with individual customers and consequently all are charged equal prices. In such a competitive pooling equilibrium, the price of each good is equal to the average of individual marginal costs weighted by equilibrium quantities. We derive modified Ramsey–Boiteux Conditions for optimum taxes in such an economy and show that, in addition to the standard formula, they include first-order effects which reflect the deviations of prices from marginal costs and the response of equilibrium quantities to the taxes levied. An explanation of the additional terms is provided. It is shown that a condition on the monotonicity of demand elasticities enables to sign the direction of the deviations from the standard case.

The Retention Effect of Withholding Performance Information

It is a common practice for firms to conduct performance evaluations of their employees and yet to withhold this information from those employees. This paper argues that firms strategically withhold performance information to retain workers. In particular, if the worker enjoys high outside options and is tempted to quit, then the firm chooses not to reveal his performance information in order to keep him on the job. The firm's equilibrium strategy is to fire if performance is sufficiently low, reveal information if performance is sufficiently high, and withhold information otherwise. The pooling equilibrium is robust under a wide variety of settings, such as general cost functions, ability-contingent outside options, nonlinear contracts, nonverifiable output, and multiple stages of production.

Learning and transfer in signaling games

We explore how learning to play strategically in one signaling game promotes strategic play in a related signaling game. Following convergence to a pooling equilibrium, payoffs are changed to only support separating equilibria. More strategic play is observed following the change in payoffs than for inexperienced subjects in control sessions, contrary to the prediction of a fictitious play learning model. Introducing a growing proportion of sophisticated learners, subjects who anticipate responders’ behavior following the change in payoffs, enables the model to capture the positive cross-game learning observed in the data.

Imperfect Signals and Product Safety Disclosure: A Shepherd's Dilemma

We study dynamic markets where product safety is unobserved by consumers. Perfect, but costly, audits and an exogenous noisy signal can provide information regarding seller type. Without the noisy signal, sellers do not disclose product safety without auditing. If audits are too expensive, a pooling equilibrium can result in consumption of unsafe goods. Even a noisy quality signal perfectly identifies unsafe goods by giving sellers incentives to disclose type without audits. Introducing a signal helps buyers, but its effect on sellers is ambiguous. Even if sellers benefit, they always suffer from increases in precision.

Insurance choice and tax-preferred health savings accounts

We develop an infinite horizon utility maximization model of the interaction between insurance choice and tax-preferred health savings accounts. The model can be used to examine a wide range of policy options, including flexible spending accounts, health savings accounts, and health reimbursement accounts. We also develop a 2-period model to simulate various implications of the model. Key results from the simulation analysis include the following: (1) with no adverse selection, use of unrestricted health savings accounts leads to modest welfare gains, after accounting for the tax revenue loss; (2) with adverse selection and an initial pooling equilibrium comprised of “sick” and “healthy” consumers, introducing HSAs can, but does not necessarily, lead to a new pooling equilibrium. The new equilibrium results in a higher coinsurance rate, an increase in expected utility for healthy consumers, and a decrease in expected utility for sick consumers; (3) with adverse selection and a separating equilibrium, both sick and healthy consumers are better off with a health savings account; (4) efficiency gains are possible when insurance contracts are explicitly linked to tax-preferred health savings accounts.

Secrecy, two-sided bias and the value of evidence

We provide necessary and sufficient conditions on players' preferences for a verifiable message game to possess a separating equilibrium and/or a pooling equilibrium, as well as sufficient conditions for every equilibrium of such a game to be pooling. We also characterize all nonseparating equilibria, and use this property to show that less information might be conveyed in any equilibrium of a verifiable message game than in some equilibrium of the cheap talk game with the same parameters.