Bribing and signaling in second price auctions

We examine whether a two-bidder, second-price auction for a single good (with private, independent values) is immune to a simple form of collusion, where one bidder may bribe the other to commit to stay away from the auction (i.e. submit a bid of zero). In either of two cases—where the potential bribe is fixed or allowed to vary—the only robust equilibria involve bribing. In the fixed-bribe case, there is a unique such equilibrium. In the variable bribes case, all robust equilibria involve low briber-types revealing themselves through the amount they offer, while all high types offer the same bribe; only one such equilibrium is continuous. Bribing in all cases causes inefficiency.     

Secure implementation experiments: Do strategy-proof mechanisms really work?

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept used in social choice theory. Saijo, Sjöström and Yamato [Saijo, T., Sjöström, T., Yamato, T., 2003. Secure implementation: Strategy-proof mechanisms reconsidered. Working paper 4-03-1. Department of Economics, Pennsylvania State University] argue that this concept has serious drawbacks. In particular, many strategy-proof mechanisms have a continuum of Nash equilibria, including equilibria other than dominant strategy equilibria. For only a subset of strategy-proof mechanisms do the set of Nash equilibria and the set of dominant strategy equilibria coincide. For example, this double coincidence occurs in the Groves mechanism when preferences are single-peaked. We report experiments using two strategy-proof mechanisms. One of them has a large number of Nash equilibria, but the other has a unique Nash equilibrium. We found clear differences in the rate of dominant strategy play between the two.     

Secure implementation experiments: Do strategy-proof mechanisms really work?

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept used in social choice theory. Saijo, Sjöström and Yamato [Saijo, T., Sjöström, T., Yamato, T., 2003. Secure implementation: Strategy-proof mechanisms reconsidered. Working paper 4-03-1. Department of Economics, Pennsylvania State University] argue that this concept has serious drawbacks. In particular, many strategy-proof mechanisms have a continuum of Nash equilibria, including equilibria other than dominant strategy equilibria. For only a subset of strategy-proof mechanisms do the set of Nash equilibria and the set of dominant strategy equilibria coincide. For example, this double coincidence occurs in the Groves mechanism when preferences are single-peaked. We report experiments using two strategy-proof mechanisms. One of them has a large number of Nash equilibria, but the other has a unique Nash equilibrium. We found clear differences in the rate of dominant strategy play between the two.     

Lobbying under political uncertainty

This paper considers a model of lobbying described as a common agency game; it departs from the current literature by assuming that the special interest groups are not a priori organized or unorganized and that the type of the politician is not common knowledge. We characterize equilibria when the choice set of the politician consists of two policies; we discuss the conditions leading to efficiency and the characteristics of the groups explaining their relative success in the process of influence. We also offer some results for the general case, including disjoint necessary and sufficient conditions for the equilibria to be efficient.     

Sequential voting with abstention

Dekel and Piccione [2000. Sequential voting procedures in symmetric binary elections. J. Polit. Economy 108, 34–55] have proven that information cascades do not necessarily affect the properties of information aggregation in sequential elections: under standard conditions, any symmetric equilibrium of a simultaneous voting mechanism is also an equilibrium of the correspondent sequential mechanism. We show that when voters can abstain, these results are sensitive to the introduction of an arbitrarily small cost of voting: the set of equilibria in the two mechanisms are generally disjoint; and the informative properties of the equilibrium sets can be ranked. If an appropriate q-rule is chosen, when the cost of voting is small the unique symmetric equilibrium of the simultaneous voting mechanism dominates all equilibria of the sequential mechanism.     

A dynamic two country Heckscher–Ohlin model with non-homothetic preferences

We examine the properties of a two-country dynamic Heckscher–Ohlin model that allows for preferences to be non-homothetic. We show that the model has a continuum of steady state equilibria under free trade, with the initial conditions determining which equilibrium will be attained. We establish conditions under which a static Heckscher–Ohlin theorem will hold in the steady state, and also conditions for a dynamic Heckscher–Ohlin theorem to hold. If both goods are normal, each country will have a unique autarkic steady state, and all steady state equilibria are saddle points. We also consider the case in which one good is inferior, and show that this can lead to multiple autarkic steady states, violations of the static Heckscher–Ohlin theorem in the steady state. Furthermore, there may exist steady state equilibria that Pareto dominate other steady states. These steady states will be unstable if discount factors are the same in each country, although they may exhibit dynamic indeterminacy if discount factors differ.     

An experimental comparison of collective choice procedures for excludable public goods

This paper compares three collective choice procedures for the provision of excludable public goods under incomplete information. One, serial cost sharing (SCS), is budget balanced, individually rational, anonymous and strategy proof. The other two are “hybrid” procedures: voluntary cost sharing with proportional rebates (PCS) and with no rebates (NR). PCS satisfies all these properties except strategy proofness, and NR satisfies all the properties except for strategy proofness and budget balance. However, PCS and NR do not exclude any potential users, and they do not require equal cost shares, thereby overcoming the two main sources of inefficiency with SCS. We characterize the Bayesian Nash equilibria (BNE) of the hybrid mechanisms and conduct laboratory experiments to compare the performance of the three mechanisms. We find that PCS produces significantly more efficient allocations than either SCS or NR.     

On trees and logs

In this paper we contrast the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), to a benchmark model in financial equilibrium theory, the real assets model (RA-Model). It is commonly believed that the two models entail similar conclusions since the LT-Model is a special case of the RA-Model. But this is simply wrong: implications of these models can be strikingly at odds. Indeed, under the widely used log-linear specification of households’ preferences, we show that for a large set of initial endowments the LT-Model—even with potentially complete financial markets—admits only peculiar financial equilibria in which the stock market is completely degenerate, in that all stocks offer the same investment opportunity—and yet, allocation is Pareto optimal. We investigate why the LT-Model is so much at variance with the RA-Model, and uncover new results on uniqueness of financial equilibria and introduction of portfolio constraints obtaining in the LT-Model, but not in the RA-Model.     

Trading with a common agent under complete information: A characterization of Nash equilibria

We analyze an abstract model of trading where N principals submit quantity-payment schedules that describe the contracts they offer to an agent, and the agent then chooses how much to trade with every principal. This represents a special class of common agency games with complete information. We study all the subgame perfect Nash equilibria of these games, not only truthful ones, providing a complete characterization of equilibrium payoffs. In particular, we show that the equilibrium that is Pareto-dominant for the principals is not truthful when there are more than two of them. We also provide a partial characterization of equilibrium strategies.     

Cooperation vs. competition in R&D: The role of stability of equilibrium

We consider a model in which firms first choose process R&D expenditures and then compete in an output market. We show the symmetric equilibrium under R&D competition is sometimes unstable, in which case two asymmetric equilibria must also exist. For the latter, we find, in contrast to the literature that total profits are sometimes higher with R&D competition than with research joint venture cartelization (due to the cost asymmetry of the resulting duopoly in the noncooperative case). Furthermore, these equilibria provide another instance of R&D-induced firm heterogeneity.     

Discrete time dynamics in a random matching monetary model

Summary. Under take-it-or-leave-it offers, dynamic equilibria in the discrete time random matching model of money are a “translation” of dynamic equilibria in the standard overlapping generations model. This formalizes earlier conjectures about the equivalence of dynamic behavior in the two models and implies the indeterminacy of dynamic equilibria in the random matching model. As in the overlapping generations model, the indeterminacy disappears if an arbitrarily small utility to holding money is introduced. We introduce a different pricing mechanism, one that puts into sharp focus that agents are forward-looking when they interact. Received: January 18, 2001; revised version: May 25, 2001     

Iterated strict dominance in general games

We offer a definition of iterated elimination of strictly dominated strategies (IESDS^*) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS^* is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS^* by means of a “stability” criterion, and offer a sufficient and necessary epistemic condition for IESDS^*. We show by an example that IESDS^* may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS^* preserves the set of Nash equilibria.     

Iterated strict dominance in general games

We offer a definition of iterated elimination of strictly dominated strategies (IESDS^*) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS^* is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS^* by means of a “stability” criterion, and offer a sufficient and necessary epistemic condition for IESDS^*. We show by an example that IESDS^* may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS^* preserves the set of Nash equilibria.     

The rate of convergence to perfect competition of matching and bargaining mechanisms

We study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information. A friction parameter is τ, the length of the time period until the next meeting. We provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in τ, which is shown to be the fastest possible among all bargaining mechanisms. The condition requires that buyers and sellers always retain some bargaining power. The bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power (NBP) mechanisms. Simple random proposer take-it-or-leave-it protocols are NBP, while k-double auctions (k-DA) are not. We find that k-DAs have equilibria that converge to perfect competition at a linear rate, converge at a slower rate or even do not converge at all.     

Government policy and the probability of coordination failures

This paper introduces an approach to the study of optimal government policy in economies characterized by a coordination problem and multiple equilibria. Such models are often criticized as not being useful for policy analysis because they fail to assign a unique prediction to each possible policy choice. We employ a selection mechanism that assigns, ex ante, a probability to each equilibrium indicating how likely it is to obtain. We show how such a mechanism can be derived as the natural result of an adaptive learning process. This approach leads to a well-defined optimal policy problem, and has important implications for the conduct of government policy. We illustrate these implications using a simple model of technology adoption under network externalities.     

Collective decisions with interdependent valuations

Many collective decision problems have in common that individuals’ desired outcomes are correlated but not identical. This paper studies collective decisions with private information about desired policies. Each agent holds private information which mainly concerns his own bliss point, but private information also affects all other agents. We concentrate on two specific mechanism, the median and mean mechanisms establish the existence of symmetric Bayesian Nash equilibria of the corresponding games and compare the performance of the mechanisms for different degrees of interdependencies. Applications of our framework include the provision of public goods and the design of decision processes in international organizations.     

Tax competition in a Bertrand model

We show that in Bertrand models pure-strategy equilibria exist only under extraordinarily restrictive assumptions. We analyze tax competition between two countries for foreign investment. In the symmetric case of equal gross profits of the firms, zero-taxation is the unique equilibrium in pure strategies. If gross profits differ between countries only -equilibria can exist. However, if the tax rate applies to foreign investment as well as to domestic sources no equilibria exist in pure strategies. The same holds true if countries compete for firms that differ in gross profit opportunities, unless extremely unrealistic conditions are met.     

Spatial Evolution of Social Norms in a Common-Pool Resource Game

We study the conditions for the emergence of cooperation in a spatial common-pool resource (CPR) game. We consider three types of agents: cooperators, defectors and enforcers. The role of enforcers is to punish defectors for overharvesting the resource. Agents are located on a circle and they only observe the actions of their two nearest neighbors. Their payoffs are determined by both local and global interactions and they modify their actions by imitating the strategy in their neighborhood with the highest average payoffs on average. Using theoretical and numerical analysis, we find a large diversity of equilibria to be the outcome of the game. In particular, we find conditions for the occurrence of equilibria in which the three strategies coexist. We also derive the stability of these equilibria. Finally, we show that introducing resource dynamics in the system favors the occurrence of cooperative equilibria.      

Efficiency versus optimality in procurement

We study procurement procedures that simultaneously determine the specification and price of a good. Suppliers can offer and produce the good in either of two possible specifications, both of which are equally good for the buyer. Production costs are interdependent and unknown at the time of bidding. Each supplier receives two signals about production cost, one per specification. Our model is a special case of the interdependent value settings with multidimensional types in Jehiel and Moldovanu (Econometrica 69:1237–1259, 2001) where an efficient and incentive compatible mechanism exists. We characterize equilibrium bidding behavior if the winning supplier is selected purely on the basis of price, regardless of the specification offered. While there is a positive chance of obtaining an inefficient specification, this procurement mechanism involves lower information rents than efficient mechanisms, suggesting that there is a trade-off between minimizing expected expenditure for the good, and ensuring that the efficient specification is chosen.