Volume 11, Issue 1

We study strategy-proof decision rules in the variant of the canonical public good model proposed by Borgers and Postl (2009). In this setup, we fully characterize the set of budget-balanced strategy-proof deterministic mechanisms, which are simple threshold rules. For smooth probabilistic mechanisms, we provide a necessary and sufficient condition for dominant strategy implementation. When allowing for discontinuities in the mechanism, our necessary condition remains valid, but additional conditions must hold for sufficiency. We also show that, among ex post efficient decision rules, only dictatorial ones are strategy-proof. While familiar in spirit, this result is not the consequence of any known result in the literature.

The make-or-buy decision is analyzed in a simple framework combining contractual incompleteness with the existence of an imperfect but contractible performance measure. Contractual incompleteness gives rise to two regimes, identified with make and buy. The performance measure on which comprehensive contracts can be written is imperfect in the sense of being subject to manipulation. The performance incentives faced by the agent are stronger in the "buy" regime. A positive (negative) impact -- or "externality" -- of manipulation on true performance favors make (buy).

We solve for the optimal mechanism for selling two goods when the buyer’s demand characteristics are unobservable. In the case of substitutable goods, the seller has an incentive to offer lotteries over goods in order to charge the buyers with large differences in the valuations a higher price for obtaining their desired good with certainty. However, the seller also has a countervailing incentive to make the allocation of the goods among the participating buyers more efficient in order to increase the overall demand. In the case when the buyer can consume both goods, the seller has an incentive to underprovide one of the goods in order to charge the buyers with large valuations a higher price for the bundle of both goods. As in the case of substitutable goods, the seller also has a countervailing incentive to lower the price of the bundle in order to increase the overall demand.

We extend the “no-haggling” result of Riley and Zeckhauser (1983) to the class of linear multiproduct monopoly problems when the buyer’s valuations are smoothly distributed. In particular, we show that there is no loss for the seller in optimizing over mechanisms such that all allocations belong to the boundary of the feasible set. The set of potentially optimal mechanisms can be further restricted when the costs are sufficiently low: the optimal mechanisms use only allocations from the “north-east” boundary of the feasible set and the null allocation.

We use an interactive epistemology framework to provide a systematic analysis of some solution concepts for games with asymmetric information. We characterize solution concepts using expressible epistemic assumptions, represented as events in the canonical space generated by primitive uncertainty about the payoff relevant state, payoff irrelevant information, and actions. In most of the paper, we adopt an interim perspective, which is appropriate to analyze genuine incomplete information. We relate Delta-rationalizability (Battigalli and Siniscalchi, Advances in Theoretical Economics 3, 2003) to interim correlated rationalizability (Dekel, Fudenberg and Morris, Theoretical Economics 2, 2007) and to rationalizability in the interim strategic form. We also consider the ex ante perspective, which is appropriate to analyze asymmetric information about an initial chance move. We prove the equivalence between interim correlated rationalizability and an ex ante notion of correlated rationalizability.

We construct laboratory financial markets in which subjects can trade an asset whose value is unknown. Subjects receive private clues about the asset value and then set bid and ask prices at which they are willing to buy or to sell from the other participants. In some of our markets (experimental treatments), there are gains from trade, while in others there are no gains: trade is zero sum. Celebrated no-trade theorems state that differences in private information alone cannot explain trade in the zero sum case. We study whether purely informational trade is eliminated in our experimental markets with no gains. The comparison of our results for gains and no-gains treatments shows that subjects fail to reach the no-trade outcome by pure introspection, but they approach it over time through market feedback and learning. Furthermore, the less noisy the clue-asset relationship is, the closer trade comes to being eliminated entirely.

In a setting with repeated experiments, where evidence about the experiments is symmetric, a decision-maker ranks bets (or acts) over their outcomes. We describe a stark modeling trade-off between symmetry of preference (indifference to permutations), dynamic consistency and ambiguity. Then, assuming that experiments are ordered in time, we outline an axiomatic model of preference that exhibits dynamic consistency and yet models learning under ambiguity.

We determine explicitly the fully nonlinear equilibrium tariffs in a simple tractable model where two firms compete for consumers whose private preferences for products and quantities are correlated because they mix both goods. Contrary to the existing literature assuming uncorrelated preferences, neither full exclusivity nor two-part tariffs can arise in equilibrium. The equilibrium tariff sorts consumers through decreasing marginal prices even when goods are almost homogeneous. The market splits endogenously between one-stop and two-stop shopping customers. This conclusion also holds when consumers differ in total demand.

I study an economy with sellers and buyers. The sellers are capacity constrained and face stochastic demand. They may locate close to each other, cluster, or separately. In the former case the buyers can visit any of them, while in the latter case the buyers can visit only one of them. The sellers post prices which are observed by the buyers who base their decision to contact sellers on the prices. I explicitly derive the equilibrium prices or price strategies in the clustered and in the non-clustered market for an arbitrary distribution of demand. I show that the clustered market often yields higher profits than the non-clustered. Finally, I allow the sellers to choose both the market and prices, and show that the equilibrium market structure features clustering.

We study a model of opinion formation and analyze the link between network architecture and the “left-right spectrum” that frequently characterizes opinions and beliefs. We correct a key result of DeMarzo, Vayanos and Zwiebel (QJE, 2003) who claim that after some time, an agent’s position on a set of different issues will always be either “left” on all of those issues or “right” on all of those issues. We provide counterexamples to this claim and show that in the long-run an agent’s position can flip-flop between “left” on all issues and “right” on all issues indefinitely. However, we provide necessary and sufficient conditions for a stable left-right characterization of opinions to be possible in the long run. Roughly, a flip-flop will occur when agents give relatively little weight to the opinions of agents with similar political positions (including themselves). Following this intuition, we show that a simple sufficient condition is that agents become “stubborn” over time and give little weight to the opinions of others. Finally, we characterize classes of networks in which it is possible for agents to flip-flop between “left” and “right” indefinitely. We argue that qualitatively, these results are robust to alternative models of opinion formation.

This paper studies a model with one principal and two agents where one agent can gather information that is valuable for the principal's project choice and the other agent provides effort to the chosen project. Defining authority as the right to choose a project and contract with the agent who does not directly contract with the principal, we ask when the principal can benefit from delegating authority to one of the agents. We show that beneficial delegation is possible when complete contracts cannot be written and authority is delegated to the information gatherer. The benefits of delegation stem from either efficiency gains or reduction in rent to the information gatherer. This can be viewed as a reasonable portrayal of a typical corporate hierarchy where top managers are delegated the authority to make strategic decisions and to contract with other employees.

The authorities often disclose their economic forecasts to the public ambiguously. The more ambiguous the way in which they present the information, the more variously market participants interpret such announcements. Hence, an ambiguous public announcement mixes some private noise to the authorities’ economic forecasts. Using Keynesian beauty contest games, as in Morris and Shin (2002), we find that mixing private noise into public information is often socially beneficial. We also derive the optimal information dissemination policy and find that (i) for a given level of ambiguity, it may be better not to release information, and (ii) if ambiguity can be chosen freely, it is optimal to release the most precise information, but with an appropriate degree of ambiguity.

How would a boundedly rational agent react to a larger menu? I model choice from an unobservable, subjective consideration subset. Consideration sets satisfy Sen’s property alpha: larger objective choice sets can generate smaller consideration sets. The contribution of this paper is a representation of choice among menus: choice sets are only as valuable as the best item in their subjective subsets, so larger sets can be worse. Unlike people facing temptation, a boundedly rational decision maker can strictly prefer both of two choice sets to their union. This model of intertemporal choice reflects how an agent who satisfies Weak WARP would choose, if sophisticated about her bounded rationality.

In an economy with a non-convex production sector, we provide an assumption on each individual producer, which implies that the survival assumption holds true at the aggregate level for general pricing rules. For the marginal pricing rule, we derive this assumption from the bounded marginal productivity of inputs. We apply this approach to intertemporal economies and we show how our assumption fits well with the time structure. We obtain a tractable existence result of equilibria for discrete time growth models.

This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mappings from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobian matrix of best-response functions has positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games. In particular, we show how the same conditions used in those theorems to show uniqueness, also guarantee existence in games with unbounded strategy spaces.

This paper investigates a two-stage competition in a vertically differentiated industry, where each firm produces an arbitrary number of similar qualities and sells them to heterogeneous consumers. The number of products, qualities, prices, and the extent of the market coverage are endogenously determined. We show that when unit costs of quality improvement are increasing and quadratic, each firm has an incentive to provide a disconnected set of similar qualities approximating a continuum. The finding contrasts sharply with the single-quality outcome when the market coverage is exogenously determined. We also show that allowing for multiple qualities intensifies the level of competition, lowers the profit of each firm, and raises the consumer surplus and the social welfare in comparison to the single-quality duopoly.

In a two-stage sequential investment problem, a principal can use either a single agent or two separate agents to execute the project. The final outcome of the project depends upon both the agent's investments and the first-stage outcome. The principal wishes to stop the project when the first stage is a failure; however, she may not know the first-stage outcome, so that she has to pay the agent a rent to extract that information. Furthermore, the first-stage agent can transmit his know-how to the second-stage agent. Although there is a transmission cost under separate agency while there is no cost under single agency, single agency is not always optimal. This is because the transmission cost can reduce the agent's incentive to continue the project so that the information rent can be lower under separate agency. Hence, the principal may prefer separate agency more even when the transmission cost becomes larger.

In many industries, it is quite common to observe firms delegating the production of essential inputs to independent ventures jointly established with competing rivals. The diffusion of this arrangement and the favourable stance of competition authorities call for the assessment of the social and private desirability of Input Production Joint Ventures (IPJV), which represent a form of input production cooperation, scantly investigated so far. IPJV can be seen as an intermediate organizational setting lying between the two extremes of vertical integration and vertical separation, with a major difference, due to partial collusion. Our investigation is based on an oligopoly model with horizontally differentiated goods. We characterize the conditions under which IPJV is privately optimal finding that firms' incentives may be welfare detrimental. We also provide a rationale for the empirical relevance of IPJV both in terms of its ability to survive and in terms of disengagement incentives which account for the large number of divorces among members of joint ventures. The stance of the paper as to IPJV is more cautious with respect to the received wisdom of competition authorities and in favour of the wide application of the rule of reason.

This paper examines a variant of the Hotelling two-stage mill-pricing duopoly game with “linear-quadratic” transport costs and the uniform customer distribution subject to a random shock. The demand is equally likely to be found anywhere in a fixed interval of feasible product characteristics, with the ex-post differentiation of tastes parametrized to reflect the degree of uncertainty. It turns out that, for uncertainty big enough, the presence of a linear component in the cost function no longer rules out an analytical solution to the game, which is a common problem in spatial competition models. In particular, a subgame-perfect equilibrium is shown to exist in which the firms’ locations approach the socially efficient ones as uncertainty further increases, regardless of the curvature of the cost function. When the demand uncertainty reaches maximum, mill-pricing is equivalent to spatial price discrimination under the most general conditions.

We apply stochastic stability to undiscounted finitely repeated two player games without common interests. We prove an Evolutionary Feasibility Theorem as an analog to the Folk Theorem (Benoit and Krishna, 1985 and 1987). Specifically, we demonstrate that as repetitions go to infinity, the set of stochastically stable equilibrium payoffs converges to the set of individually rational and feasible payoffs. This derivation requires stronger assumptions than the Nash Folk Theorem (Benoit and Krishna, 1987). It is demonstrated that the stochastically stable equilibria are stable as a set, but unstable as individual equilibria. Consequently, the Evolutionary Feasibility Theorem makes no prediction more specific than the entire individually rational and feasible set.

This study investigates the choice between complementary and parallel alliances in a market with vertical and horizontal externalities. One composite goods firm competes with two components producers, each providing a complementary component of a differentiated composite good. Although the joint profits from a parallel alliance between the composite goods firm and a components producer are always larger than those from a complementary alliance between components producers, through Nash bargaining, a components producer prefers the complementary (parallel) alliance when the degree of product differentiation is sufficiently large (small). Combined with the result that a complementary alliance is socially preferable, our findings provide meaningful implications for antitrust policy.

This paper constructs and analyzes open-loop equilibria in an infinitely repeated Tullock contest in which two contestants contribute efforts to accumulate individual asset stocks over time. To investigate the transitional dynamics of the contest in the case of a general cost function, we linearize the model around the steady state. Our analysis shows that optimal asset stocks and their speed of convergence to the steady state crucially depend on the elasticity of marginal effort costs, the discount factor and the depreciation rate. In the case of a cost function with a constant elasticity of marginal costs, a lower discount factor, a higher depreciation rate and a lower elasticity imply a higher speed of convergence to the steady state. We further analyze the effects of second prizes in the contest. A higher prize spread increases individual and aggregate asset stocks, but does not alter the balance of the contest in the long run. During the transition, a higher prize spread increases asset stocks, produces a more balanced contest in each period and increases the speed of convergence to the steady state.

Recent work in several fields has established that humans can adopt binding “behavioral” preferences and convincingly signal those preferences to other humans, either via their behavior or via their body language / tone of voice. In this paper, we model the strategic implications of this ability. Our thesis is that through a person's lifetime they (perhaps subconsciously) learn what such signaled, binding behavioral preferences result in the highest value of their actual preferences, given the resultant behavior of other players. We argue that this “persona” model may explain why many interpersonal preferences have the particular form they do. As an illustration, we use the persona model to explain cooperation in non-repeated versions of the Prisoner's Dilemma (PD). We also provide quantitative predictions to distinguish this explanation of cooperation from simply assuming people have actual preferences biased towards cooperation. In particular, we show that the persona model predicts a “crowding out” phenomenon in the PD, in which introducing incentives to cooperate causes players to stop cooperating instead. We also use the persona model to predict a tradeoff between the robustness of cooperation in the PD and the benefit of that cooperation.

This paper presents mechanisms implementing the core correspondence of many-to-one matching markets, such as college admissions problems, where the students have preferences over the other students who would attend the same college. We first present a sequential mechanism implementing the core. We then show that simple two-stage mechanisms, which mimics the real-life processes, cannot be used to implement the core correspondence in subgame perfect Nash equilibrium even with strong assumptions on agents’ preferences.