Impossibility of stable and nonbossy matching mechanisms

Stability is a central concept in matching theory, while nonbossiness is important in many allocation problems. We show that these properties are incompatible: there does not exist a matching mechanism that is both stable and nonbossy.     

Incentives in two-sided matching with random stable mechanisms

Summary This paper considers the incentives confronting agents who face the prospect of being matched by some sort of random stable mechanism, such as that discussed in Roth and Vande Vate (1990). A one period game is studied in which all stable matchings can be achieved as equilibria in a natural class of undominated strategies, and in which certain unstable matchings can also arise in this way. A multi-period extension of this game is then considered in which all subgame perfect equilibria must result in stable matchings. These results suggest avenues to explore markets in which matching is organized in a decentralized way.     

Time and uncertainty in resource dilemmas: equilibrium solutions and experimental results

Most common pool resource (CPR) dilemmas share two features: they evolve over time and they are managed under environmental uncertainties. We propose a stylized dynamic model that integrates these two dimensions. A distinguishing feature of our model is that the duration of the game is determined endogenously by the users’ collective decisions. In the proposed model, if the resource stock level below which the irreversible event occurs is known in advance, then the optimal resource use coincides with a unique symmetric equilibrium that guarantees survival of the resource. As the uncertainty about the threshold level increases, resource use increases if users adopt decision strategies that quickly deplete the resource stock, but decreases if they adopt path strategies guaranteeing that the unknown threshold level is never exceeded. We show that under relatively high uncertainty about resource size, CPR users frequently implement decision strategies that terminate the game immediately. When this uncertainty is reduced, they maintain a positive resource level for longer durations.     

Attitudes to risk and attitudes to uncertainty: experimental evidence

In a series of experiments the interactions among individual attitudes towards risk and uncertainty, the sign of the outcome domain, and the way uncertainty is represented are tested. This is done in a unified framework, eliciting individual values by means of a second price auction. Results confirm the presence of the well-known fourfold pattern of risk attitude (risk aversion for gains and risk seeking for losses at high probability, and risk seeking for gains and risk aversion for losses at low probability) and show that this pattern can also be extended to uncertainty. In the valuation of losses the modal pattern is decreasing risk and uncertainty aversion as the probability of loss increases, while increasing risk and uncertainty aversion is observed for gains. Moreover, it is found that the size of reaction to uncertainty does not depend on the outcome domain, and that it persists in the face of an incentive-compatible mechanism to elicit preferences.     

Gaining power through enlargement: Strategic foundations and experimental evidence

Power indices suggest that adding new members to a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the original members may actually gain even if voters are bargaining over a fixed budget. We show that this phenomenon can occur as an equilibrium of a non-cooperative bargaining game based on the Baron and Ferejohn (1989) model of legislative bargaining. We implement this game in the laboratory and find that power can be gained by adding new members as the theory predicts.     

Strategic pattern recognition—experimental evidence

The repeated play of an asymmetric Battle of the Sexes is analyzed from the perspective of “strategic pattern recognition.” Convergence to equilibrium patterns (in finite histories) and related concepts like breaking-an-equilibrium-pattern are defined and applied to the data. More than half of 202 pairs of subjects are characterized as weakly converging to a fixed equilibrium pattern. The results also show that subjects tend to break their best pattern in cases where their partners' payoffs are relatively low and that convergence initiation does not pay off. While female subjects frequently reject the males' best equilibrium with anonymous matching, behavior gets more cooperative when pairs are introduced to each other before the beginning of the game.     

Signaling without a common prior: Results on experimental equilibrium selection

The common prior assumption is pervasive in game-theoretic models with incomplete information. This paper investigates experimentally the importance of inducing a correct common prior in a two-person signaling game. Equilibrium selection arguments predict that different equilibria may be selected depending on whether the common prior is induced or not. Indeed, for a specific probability distribution of the sender?s type, the long-run behavior without an induced common prior is shown to be different from the long-run behavior when a common prior is induced, while for other distributions long-run behavior is similar under both regimes. We also present a learning model that allows players to learn about the other players? strategies and the prior distribution of the sender?s type. We show that this learning model accurately accounts for all main features of the data.     

Procedurally fair and stable matching

Summary. We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al. , 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism, that combines aspects of procedural and endstate fairness.Received: 9 September 2003, Revised: 12 December 2004, JEL Classification Numbers: C78, D63. Correspondence to: Flip KlijnWe thank two referees and a co-editor for helpful comments and suggestions. B. Klauss and F. Klijns research has been supported by Ramón y Cajal contracts of the Spanish Ministerio de Ciencia y Tecnología. The work of the authors has also been partially supported by Research Grant BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and by the Barcelona Economics Program of CREA. This paper is part of the Polarization and Conflict Project CIT-2-CT-2004-506084 funded by the European Commission-DG Research Sixth Framework Programme. This article reflects only the authors views and the Community is not liable for any use that may be made of the information contained therein.     

Network formation and stable equilibrium

We study the non-cooperative formation of a (directed) network that builds upon one-way immediate links. Our novel feature is that we require circular paths of links for productive activities. This captures more clearly the higher level of coordination that is often required for network formations than models such as those of Jackson and Wolinsky [A strategic model of social and economic networks, J. Econ. Theory 71 (1996) 44-74] and Bala and Goyal [A non-cooperative model of network formation, Econometrica 68 (2000) 1181-1229], in that in our model a single agent's unilateral action is limited in affecting the network structure. We completely characterize the class of Nash equilibria by showing that the minimality of a graph is both necessary and sufficient (Theorem 1). We also propose the concept of a stable network that is similar to the pairwise stability of Jackson and Wolinsky (1996). We show that stable equilibria are a wheel, a trivial network, or a sub-wheel partitioned network (Theorem 2). We modify the Bala and Goyal (2000) dynamic process with inertia, and obtain the convergence to stable equilibria regardless of the initial state (Theorem 3).     

Increasing risk and equilibrium under uncertainty

The impact of increasing risk on social welfare and resource allocation is analysed in a general equilibrium model with endowment uncertainty. It is shown that the equilibrium allocation of resources is affected only by an increase in those risks which are important for society as a whole. In contrast, increases in purely individual risk do not influence achievable social welfare and have no effect on the utility of traders in a competitive market.     

Equilibrium selection in similar repeated games: experimental evidence on the role of precedents

We report on an experiment examining behavior and equilibrium selection in two similar, infinitely repeated games, Stag Hunt and Prisoner’s Dilemma under anonymous random matching. We are interested in the role that historical precedents may play for equilibrium selection between these two repeated games. We find that a precedent for efficient play in the repeated Stag Hunt game does not carry over to the repeated Prisoner’s Dilemma game despite the possibility that efficient play can be sustained as an equilibrium of the indefinitely repeated game. Similarly, a precedent for inefficient play in the repeated Prisoner’s Dilemma game does not extend to the repeated Stag Hunt game. We conclude that equilibrium selection between similar repeated games may have less to do with historical precedents and might instead depend more on strategic considerations associated with the different payoffs of these similar repeated games.     

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.     

Ambiguity,uncertainty aversion and equilibrium welfare

Summary. In order to analyse the effect of ambiguity and uncertainty aversion on equilibrium welfare, a two period, pure exchange one good economy is considered. Agents are Choquet-expected-utility maximizers with same convex capacity and strictly concave utility index. It is proven that equilibrium is indeterminate whenever several probabilities in the core of the capacity minimize the expected value of aggregate endowment and not all agents have same expected endowments under those probabilities. It is further shown that small changes in aggregate endowment may have drastic welfare implications. A more general model is considered in the case of no aggregate uncertainty: agents have a set of priors and are uncertainty averse as modelled by Gilboa-Schmeidler [1989]. In the case of complete markets, it is shown that assets have a spread of equilibrium prices similar to the spread of no-arbitrage prices compatible with absence of arbitrage in markets with imperfections.Received: 2 June 2000, Revised: 27 March 2003, JEL Classification Numbers: D46, D59,D60, G12.I have benefited from conversations with L. Epstein, F. Magnien and J. M. Tallon.     

Waiting times and equilibrium selection

Summary. This paper shows how graphs can be used to calculate waiting times in models of equilibrium selection. It also shows how reducing the state space can simplify the calculations of both waiting times and selected equilibria. The results are applied to potential games and games with strategic complementarities.Received: 31 December 2002, Revised: 25 October 2003, JEL Classification Numbers: C72, C73.Alan Beggs: I am grateful to an anonymous referee for helpful comments.     

Strategic debt in vertical relationships: theory and evidence

We model a vertical relationship between two firms. Our main finding is that the downstream firm manipulates the extent of its debt in order to affect in its favour the contract offered by the upstream firm. Except for a very high interest rate, we find a conflict of interest between the two firms with regard to the extent of debt. This can be interpreted as a rationale for the constraint imposed by franchisors on the debt level of their franchisees. The theoretical analysis is tested using a dataset combining both survey and balance sheet data. We find evidence suggesting that debt may play a strategic role for those firms involved in close-knit vertical relationships.     

Von Neumann-Morgenstern stable sets in matching problems

The following properties of the core of a one-to-one matching problem are well-known: (i) the core is non-empty; (ii) the core is a distributive lattice; and (iii) the set of unmatched agents is the same for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (Von Neumann-Morgenstern) stable sets in one-to-one matching problems. We show that a set V of matchings is a stable set of a one-to-one matching problem only if V is a maximal set satisfying the following properties: (a) the core is a subset of V; (b) V is a distributive lattice; and (c) the set of unmatched agents is the same for all matchings belonging to V. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b), and (c).     

Strategy-proofness in experimental matching markets

We introduce two novel matching mechanisms, Reverse Top Trading Cycles (RTTC) and Reverse Deferred Acceptance (RDA), with the purpose of challenging the idea that the theoretical property of strategy-proofness induces high rates of truth-telling in economic experiments. RTTC and RDA are identical to the celebrated Top Trading Cycles (TTC) and Deferred Acceptance (DA) mechanisms, respectively, in all their theoretical properties except that their dominant-strategy equilibrium is to report one’s preferences in the order opposite to the way they were induced. With the focal truth-telling strategy being out of equilibrium, we are able to perform a clear measurement of how much of the truth-telling reported for strategy-proof mechanisms is compatible with rational behaviour and how much of it is caused by confused decision-makers following a default, focal strategy without understanding the structure of the game. In a school-allocation setting, we find that roughly half of the observed truth-telling under TTC and DA is the result of naïve (non-strategic) behaviour. Only 14–31% of the participants choose actions in RTTC and RDA that are compatible with rational behaviour. Furthermore, by looking at the responses of those seemingly rational participants in control tasks, it becomes clear that most lack a basic understanding of the incentives of the game. We argue that the use of a default option, confusion and other behavioural biases account for the vast majority of truthful play in both TTC and DA in laboratory experiments.

     

Fast convergence in evolutionary equilibrium selection

Stochastic best response models provide sharp predictions about equilibrium selection when the noise level is arbitrarily small. The difficulty is that, when the noise is extremely small, it can take an extremely long time for a large population to reach the stochastically stable equilibrium. An important exception arises when players interact locally in small close-knit groups; in this case convergence can be rapid for small noise and an arbitrarily large population. We show that a similar result holds when the population is fully mixed and there is no local interaction. Moreover, the expected waiting times are comparable to those in local interaction models.     

Correlated quantal responses and equilibrium selection

This paper considers incomplete information games with payoffs subject to correlated random disturbances. It explains the connection between the uniqueness of quantal response equilibria, where large noise is required, and the uniqueness of equilibria in global games, where small noise is required.     

Correlated quantal responses and equilibrium selection

This paper considers incomplete information games with payoffs subject to correlated random disturbances. It explains the connection between the uniqueness of quantal response equilibria, where large noise is required, and the uniqueness of equilibria in global games, where small noise is required.