Endogenous entry in auctions with negative externalities

In this paper, we study the auction to allocate an indivisible good when each potential buyer has a private and independent valuation for the item and suffers a negative externality if a competitor acquires it. In that case, the outside option of each buyer is mechanism-dependent, which implies that participation is endogenous. As several works in the literature have shown, the optimal auction entails strong threats to induce full entry and maximal expected revenue. This results from the full commitment assumption, which ensures that threats are credible. We show that absent credible threats, the entry process does not lead to full participation: the equilibrium entails screening of agents in the entry stage and a trade-off between reserve prices and entry fees. Besides, we discuss the conditions under which the impossibility to use threats does not prevent the seller from ensuring a minimal screening and reaching a high expected revenue.     

Experimental markets for insurance

This article extends the large amount of research on double-oral auction markets to hazards that produce only losses. We report results from a series of experiments in which subjects endowed with low-probability losses can pay a premium for insurance protection. Insurers specify the price at which they are willing to assume the risk of a loss. Insurance prices approach expected value for a large range of probabilities and loss amounts. Subjects seem to realize losses are statistically independent. Prices are not affected by ambiguity about the probability of loss.     

Inducing risk-neutral preferences: An examination in a controlled market environment

This article reports 15 first-price auction experiments, each with four bidders, designed to test Cedric Smith' (1961) hypothesis that risk-neutral behavior can be induced in subjects' decisions by paying them in lotteries on money that are linear in the outcome probabilities. We choose the first-price auction environment because of its relatively high success in surviving a large number of tests, which contrasts with the widely documented tendency of subjects to violate the expected utility axioms in making choices among gambles. In the first five experiments, subjects were experienced in first-price auctions with monetary rewards. We prescreened these subjects for exceptionally high bidding consistency with the constant relative risk-averse model. The results unyielded only weak support for the risk-neutralizing procedure (3 of 10 risk-averse cases became risk-neutral, but only 1 in 8 that were retested continued to exhibit risk-neutral behavior). We recruited 16 new subjects with no previous experience for four lottery-only auctions. Eight of the 16 subjects bid as if risk-neutral, but in a retest of 12 subjects only 2 remained consistently risk-neutralized. Finally we recruited 12 inexperienced subjects, and each subject bid against 3 robot bidders whose bidding strategies were known to the human bidder. We use this procedure to control for Nash expectations. These 12 subjects were run under both monetary and lottery reward conditions. Two of the 12 subjects bid as if risk-neutral in the lottery auction, but both of these subjects had shown risk-neutral behavior with monetary rewards. In conclusion, we find very weak support for the risk-neutralizing procedure. We caution other researchers to run calibration tests of the procedure in the particular context they are studying to assess its reliability.     

Implementing egalitarianism in a class of Nash demand games

We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to \(1-x\), where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four.     

A general equilibrium model of domestic commerce in Mexico

In this paper we develop a general equilibrium model of the Mexican economy that focuses on the commercial sector, particularly retailing. Consumers purchase goods in different retail establishments, that sell differentiated goods at different prices. Where each consumer decides to make purchases depends on various price and locational considerations. The model has been calibrated to replicate the Mexican economy in 1977, the latest year for which a complete data set is available. We use it to analyze both the impact of the 1980 fiscal reform, a major policy charge for the economy as a whole, and that of a hypothetical development project aimed specifically at the commercial sector. Although our model was conceived and developed well prior to the current period of highly inflationary policies of the debt crisis, the latter was taken into consideration during both the simulations and their policy evaluation.     

Risk-adjusted martingales and the design of “indifference” gambles

In the probability literature, a martingale is often referred to as a “fair game.” A martingale investment is a stochastic sequence of wealth levels, whose expected value at any future stage is equal to the investor’s current wealth. In decision theory, a risk neutral investor would therefore be indifferent between holding on to a martingale investment, and receiving its payoff at any future stage, or giving it up and maintaining his current wealth. But a risk-averse decision maker would not be indifferent between a martingale investment and his current wealth level, since he values uncertain deals less than their mean. A risk seeking decision maker, on the other hand, would readily accept a martingale investment in exchange for his current wealth, and would repeat this investment any number of times. These ideas lead us to introduce the notion of a “risk-adjusted martingale”; a stochastic sequence of wealth levels that a rational decision maker with any attitude toward risk would value constantly with time, and would be indifferent between receiving its pay-off at any future stage, or giving it up and maintaining his current wealth level. We show how to construct such risk-adjusted investments for any decision maker with a continuous monotonic utility function. The fundamental result we derive is that a pay-off structure of an investment (i) is a risk-adjusted martingale and (ii) can be represented by a lattice if and only if the pay-off functions are invariant transformations of the given utility function.     

Exchange rate systems and relative prices

The article relaxes one of the assumptions required for exchange-rate-system neutrality, without abandoning flexible prices. It assumes that taxes or restrictions on international transactions are expected to differ under pegged and flexible exchange rates. Governments are more willing to impose restrictions or taxes when they have a low level of international reserves and operate under a system of pegged exchange rates where further losses are possible. Expectations about these policy reactions change the behavior of equilibrium relative prices: they may vary less under pegged than under flexible exchange rates, as they appear to do in the real world.     

Catastrophic flooding and the response of the real estate market

In February 1986, the levee of the Yuba River broke, flooding the towns of Linda and Olivehurst in northern California. Besides the personal tragedies, were economic disasters. Property values of the houses plummeted. While theories of natural hazards predict that the market will capitalize the risk of flooding into the value of residential property, in areas where the probability is low the risk may be ignored. Factors are the history of past floods, socioeconomic conditions, and the real estate market. Housing prices in Linda and Olivehurst did drop (effectively to zero) immediately after the flood, then recovered relatively quickly to a level significantly lower than before the catastrophe. This suggests that the previous prices did not fully capitalize the risk of this intermittent hazard.     

The curse of hope

In K?szegi and Rabin’s (Q J Econ 1133–1165, 2006, Am Econ Rev 97:1047–1073, 2007) reference-dependent model of preferences, the chance of obtaining a better outcome can reduce an agent’s expected utility through an increase in the stochastic reference point. This means that individuals may prefer stochastically dominated lotteries. In this sense, hope, understood as a small probability of a better outcome, can be a curse. While K?szegi and Rabin focus on a linear specification of the utility function, we show that this effect occurs more broadly. Using fairly plausible assumptions and parameter values, we specify the conditions under which it occurs, as well as the type of lotteries in which this should be expected. We then show that while a simple subjective transformation of probability into weights of the reference point may in some cases mitigate the issue, in others, it can intensify it or even generate new ones. Finally, we extend the model by adding the individual’s current reference point (status quo) to the stochastic reference point. We show that this modification can reconcile K?szegi and Rabin’s model with the apparent empirical infrequency of stochastically dominated choices while maintaining its main qualitative results.     

Varying the number of bidders in the first-price sealed-bid auction: experimental evidence for the one-shot game

The paper reports experimental data on the behavior in the first-price sealed-bid auction for a varying number of bidders when values and bids are private information. This feedback-free design is proposed for the experimental test of the one-shot game situation. We consider both within-subjects and between-subjects variations. In line with the qualitative risk neutral Nash equilibrium prediction, the data show that bids increase in the number of bidders. However, in auctions involving a small number of bidders, average bids are above, and in auctions involving a larger number of bidders, average bids are below the risk neutral equilibrium prediction. The quartile analysis reveals that bidding behavior is not constant across the full value range for a given number of bidders. On the high value quartiles, however, the average bid–value ratio is not different from the risk neutral prediction. The behavior is different when the winning bid is revealed after each repetition.     

Single-year and multi-year insurance policies in a competitive market

This paper examines the demand and supply of annual and multi-year insurance contracts with respect to protection against a catastrophic risk in a competitive market. Insurers who offer annual policies can cancel policies at the end of each year and change the premium in the following year. Multi-year insurance has a fixed annual price for each year and no cancellations are permitted at the end of any given year. Homeowners are identical with respect to their exposure to the hazard. Each homeowner determines whether or not to purchase an annual or multi-year contract so as to maximize her expected utility. The competitive equilibrium consists of a set of prices where homeowners who are not very risk averse decide to be uninsured. Other individuals demand either single-year or multi-year policies depending on their degree of risk aversion and the premiums charged by insurers for each type of policy.     

The Value of a Probability Forecast from Portfolio Theory

A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “market” (all available forecasts). A forecast is seen to be more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easy” trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honest” alternative to the ruse of reporting conservative probability assessments.     

Nash Equilibrium with Lower Probabilities

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings.     

Asymmetric endogenous prize contests

We consider a two-player contest in which one contestant has a headstart advantage, but both can exert further effort. We allow the prize to depend on total performance in the contest and consider the respective cases in which efforts are productive and destructive of prize value. When the contest success function takes a logit form, and marginal cost is increasing in effort, we show that a Nash equilibrium exists and is unique both in productive and destructive endogenous prize contests. In equilibrium, the underdog expends more resources to win the prize, but still his probability of winning remains below that of the favorite. In a productive contest, the underdog behaves more aggressively and wins the prize more often in comparison to a fixed-value contest. Thus, the degree of competitive balance—defined as the level of uncertainty of the outcome—depends upon the (fixed or endogenous) prize nature of the contest.     

A note on Savage's theorem with a finite number of states

This article gives a preference-based characterization of subjective expected utility for the general equilibrium model with a finite number of states. The characterization follows Savage (1954) as closely as possible but has to abandon his axiom (P6), atomlessness of events, since this requires an infinite state space. To introduce continuity we replace (P6) with a continuity assumption on the set of consequences and assume the preferences are smooth. Then we apply Savage's sure-thing principle and his state-independence axiom to get an additively separable utility representation. Finally, to separate subjective probabilities from basic tastes, we apply a new axiom, which states that for each pair of states the marginal rate of substitution is constant along the certainty line.     

FORWARD INDUCTION IN GAMES WITH AN OUTSIDE OPTION

We provide eductive foundations for the concept of forward induction, in the class of games with an outside option. The formulation presented tries to capture in a static notion the rest point of an introspective process, achievable from some restricted preliminary beliefs. The former requisite is met by requiring the rest point to be a Nash equilibrium that yields a higher payoff than the outside option. With respect to the beliefs, we propose the Incentive Dominance Criterion. Players should consider one action more likely than another whenever the former is better than getting the outside option for more conjectures over his rival's actions. We apply this model to the case where the subgame is a coordination game with a conflict between payoff dominance and risk dominance. Our results provide support for dominance solvability, but not for Van Damme's notion of forward induction. We show how the forward induction logic helps to select the Pareto dominant equilibrium. This is the case whenever player 1's act of giving up the outside option reverses the incentive dominance relations among 1's pure actions in the subgame.     

Rewarding Trust: An Experimental Study

The issue of trust has recently attracted growing attention in research on work relations, capital – owner relations, cultural influences on the economic structures of different countries, and other topics. This paper analyzes a simple experiment on trust and the reward of trust. Mr A is endowed with DM 80. He decides to trust Ms B (and give her his money) or not. Ms B is able to double the sum of money (if she gets it) and can then decide to give back as much as she likes. In an experiment, 76% of subjects A decided to trust. The average reward they received was DM 79.2 which is not significantly different from DM 80, the value of mistrust; nor was the average reward different from the average expectations of subjects A, i.e. a weak variant of the Rational Expectations Hypothesis is supported. In the paper we also look for differences between trusting and mistrusting A-subjects, for behavioral norms, and other determinants of rewards.     

Resolving Rabin’s paradox

We present a theoretical model of Rabin’s famous calibration paradox that resolves confusions in the literature and that makes it possible to identify the causes of the paradox. Using suitable experimental stimuli, we show that the paradox truly violates expected utility and that it is caused by reference dependence. Rabin already showed that utility curvature alone cannot explain his paradox. We, more strongly, do not find any contribution of utility curvature to the explanation of the paradox. We find no contribution of probability weighting either. We conclude that Rabin’s paradox underscores the importance of reference dependence.

     

Who gains from information asymmetry?

This article considers an asymmetric contest with incomplete information. There are two types of players: informed and uninformed. Each player has a different ability to translate effort into performance in terms of the contest success function. While one player’s type is known to both players, the other is private information and known only to the player himself. We compare the Bayesian Nash equilibrium outcome of a one-sided private information contest to the Nash equilibrium with no private information, in which both players know the type of the other player. We show conditions under which uncertainty increases the investment of the uninformed player and the rent dissipation of the contest, while decreasing the expected net payoff of the informed player. In addition, we consider conditions under which the informed player—before knowing his own type—prefers that the uninformed player knows his type. Moreover, we show conditions for the existence/non-existence of equilibrium in a two-stage contest in which the informed player declares his type (or does not declare) in the first stage and in the second stage the two players play according to the information available to them.     

Two-person sequential bargaining behavior with exogenous breakdown

We examine bargaining behavior in a noncooperative game in which players alternate in making and responding to proposals over the division of a given surplus. Although the number of bargaining periods is unlimited and time is not discounted, the bargaining is subject to exogenous breakdown at each period with a fixed probability which is common knowledge. We manipulate three probabilities of break-down in a between-subjects design that allows comparison with previous studies of two-person bargaining with time discounting. Assuming that subjects maximize expected utility, and this utility is measured by monetary payoffs, our results reject both the subgame perfect equilibrium and equal split solutions. Data analyses reveal that a substantial percentage of subjects behave adaptively in that they systematically search for the highest acceptable demands.