Additive values and market equilibrium

This letter is based on the simple observation that in equilibrium, values must be additive, i.e., the value of a basket of goods is equal to the sum of the values of the items contained in the basket. The observation combined with the conditions of Pareto optimality, gives an easy way to many well known results in the theory of equilibrium under uncertainty.     

Strategic complementarities and search market equilibrium

In this paper, we apply supermodular game theory to the equilibrium search literature with sequential search. We identify necessary and sufficient conditions for the pricing game to exhibit strategic complementarities and prove existence of equilibrium. We then show that price dispersion is inherently incompatible with strategic complementarities in the sense that the Diamond Paradox obtains when firms are identical and is robust within the class of search cost densities that are small near zero and support strategic complementarities. We also show that a major criticism of the literature, that agents act as if they know the distribution of prices, can be justified in the sense of convergent best response dynamics.     

Labor market equilibrium under nonsequential search

This study presents a full model of the labor market under imperfect information. Workers bear the burden of search and are assumed to use a stochastic variant of an optimal sample size search strategy. The existence and uniqueness of a nondegenerate equilibrium distribution of wage offers is established. Infficiencies which lead to underinvestment in search are uncovered and analyzed.     

Asset illiquidity and market shutdowns in competitive equilibrium

This paper introduces asymmetric information in a competitive asset market into a dynamic general-equilibrium model with borrowing constraints. In the presence of borrowing constraints, asset sales become a crucial means for agents to finance opportunities to invest in new assets. In this environment, reduced asset sales due to asymmetric information lower the economic growth rate if agents invest in new assets. The volume of asset trade, however, becomes zero if and only if agents stop investing in new assets because of sufficiently low aggregate productivity. A low economic growth rate with a market shutdown is solely due to low aggregate productivity without any role of the market shutdown.     

Honesty in tournaments

We apply the die rolling experiment of Fischbacher and Föllmi-Heusi (2013) to a two-player tournament incentive scheme. Our treatments vary the prize spread. The data highlights that honesty is more pronounced when the prize spread is small.     

Asymptotic methods for asset market equilibrium analysis

Summary. General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small. Received: April 1, 2000; revised version: January 10, 2001     

Competitive equilibrium in the credit market under asymmetric information

We study a competitive credit market equilibrium in which all agents are risk neutral and lenders a priori unaware of borrowers' default probabilities. Admissible credit contracts are characterized by the credit granting probability, the loan quantity, the loan interest rate and the collateral required. The principal result is that in equilibrium lower risk borrowers pay higher interest rates than higher risk borrowers; moreover, the lower risk borrowers get more credit in equilibrium than they would with full information. No credit is rationed and collateral requirements are higher for the lower risk borrowers.     

Asset market equilibrium with short-selling and differential information

We introduce differential information in the asset market model studied by Cheng J Math Econ 20(1):137–152,1991, Dana and Le Van J Math Econ 25(3):263–280,1996 and Le Van and Truong Xuan J Math Econ 36(3): 241–254, 2001. We prove an equilibrium existence result assuming that the economy’s information structure satisfies the conditional independence property. If private information is not publicly verifiable, agents have incentives to misreport their types and therefore contracts may not be executed in the second period. We also show that under the conditional independence property equilibrium contracts are always executable.     

Termination of dynamic contracts in an equilibrium labor market model

In an equilibrium model of the labor market, workers and firms enter into dynamic contracts that can potentially last forever, but are subject to optimal terminations. Upon termination, the firm hires a new worker, and the worker who is terminated receives a termination contract from the firm and is then free to go back to the labor market to seek new employment opportunities and enter into new dynamic contracts. The model permits only two types of equilibrium terminations that resemble, respectively, the two kinds of labor market separations that are typically observed in practice: involuntary layoffs and voluntary retirements. The model allows for the simultaneous determination of a large set of important labor market variables including equilibrium unemployment and labor force participation. An algorithm is formulated for computing the model's equilibria. I then simulate the model to show quantitatively that the model is consistent with a set of important stylized facts of the labor market.     

Multiple equilibrium overnight rates in a dynamic interbank market game

We analyse a two-period model of the interbank market, i.e. the market where banks trade liquidity. We assume that banks do not take the interbank interest rate as given, but instead negotiate on interest rates and transaction volumes with each other. The solution concept applied is the Shapley value. We show that there are a multiplicity of average equilibrium interest rates of the first period so that the average interest rate in this period does not convey any information on the expected liquidity situation on the interbank market. As the banks control not only the transaction volumes, but also the interest rates, they can leave the interest rates constant and adjust the transaction volumes when, for example, a liquidity deficit becomes more likely.     

Fairness and desert in tournaments

We model the behavior of agents who care about receiving what they feel they deserve in a two-player rank-order tournament. Perceived entitlements are sensitive to how hard an agent has worked relative to her rival, and agents are loss averse around their meritocratically determined endogenous reference points. In a fair tournament sufficiently large desert concerns drive identical agents to push their effort levels apart in order to end up closer to their reference points on average. In an unfair tournament, where one agent is advantaged, the equilibrium is symmetric in the absence of desert, but asymmetric in the presence of desert. We find that desert concerns can undermine the standard conclusion that competition for a fixed supply of status is socially wasteful and explain why, when the distribution of output noise is fat-tailed, an employer might use a rank-order incentive scheme.     

Minimal stable sets in tournaments

We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set.     

Optimal seedings in elimination tournaments

We study an elimination tournament with heterogenous contestants whose ability is common-knowledge. Each pair-wise match is modeled as an all-pay auction. Equilibrium efforts are in mixed strategies, yielding complex dynamics: endogenous win probabilities in each match depend on other matches’ outcome through the identity of the expected opponent in the next round. The designer seeds competitors according to their ranks. For tournaments with four players we find optimal seedings for three different criteria: (1) maximization of total tournament effort; (2) maximization of the probability of a final among the two top ranked teams; (3) maximization of the win probability for the top player. We also find the seedings ensuring that higher ranked players have a higher winning probability. We compare our predictions with data from NCAA basketball tournaments.