We consider a game in extensive form recurrently played by agents who are randomly drawn from large populations and matched. We assume that preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff, Marinacci, and Mukerji (Econometrica, 2005), which may induce dynamic inconsistencies. We take this into account in our analysis of self-confirming equilibrium (SCE) given players' feedback about the path of play. Battigalli, Cerreia-Vioglio, Maccheroni, and Marinacci (Amer. Econ. Rev., 2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for SCE.
We experimentally study sequential procurement auctions where bidders' capacity constraints are private information. Our experiment involves two first-price auctions with a belief elicitation stage at the end of the first. Our results show that (i) observed behavior in the second auction is overall consistent with sequential rationality; (ii) first auction bids are decreasing in the capacity of the bidder, but (iii) stated beliefs are inconsistent with the actual play. Hence, subjects seem to be aware of the opportunity cost of early bids (which leads capacity constrained bidders to bid more cautiously than unconstrained ones); on the other hand, since they do not recognize the informative content of bids, the potential signaling cost associated with early bids does not come into play.
There is by now a large literature arguing that auctions with a variety of after-market interactions may not yield an efficient allocation of the objects for sale, especially when the bidders impose strong negative externalities upon each other. In this note, we argue that these inefficiencies can be avoided by asking bidders prior to the auction to submit any publicly observable payment they would like to make. These payments, so-called flexible entry fees, do not affect the allocation decision of the auctioneer. We show that auctions with flexible entry fees have a fully revealing equilibrium where bidders signal their type before the auction itself takes place.
Financial constraints reduce the lawyer's ability to file lawsuits and bring cases to trial. As a result, access to justice for victims, pretrial bargaining, and potential injurers' precaution might be affected. We study civil litigation using a model that allows for asymmetric information, financially-constrained lawyers, third-party lawyer lending, and a continuum of plaintiff's types. We contribute to the economic analysis of law by generalizing seminal models of litigation (Bebchuk, 1984, Bebchuk, 1988; Katz, 1990), offering the first formal definition of access to justice, and presenting comprehensive social welfare analysis of relevant public policy. We provide complete equilibrium characterization and identify necessary conditions for the existence of the mixed- and pure-strategy PBE. Access to justice is denied to some victims under the mixed-strategy equilibrium. We then study the social welfare effects of policies aimed at relaxing lawyers' financial constraints, and identify a necessary and sufficient condition for a welfare-enhancing effect.
Strong-Δ-Rationalizability introduces first-order belief restrictions in the analysis of forward induction reasoning. Without actual restrictions, it coincides with Strong Rationalizability (Battigalli, 2003; Battigalli and Siniscalchi, 2003). These solution concepts are based on the notion of strong belief (Battigalli and Siniscalchi, 2002). The non-monotonicity of strong belief implies that the predictions of Strong-Δ-Rationalizability can be inconsistent with Strong Rationalizability. I show that Strong-Δ-Rationalizability refines Strong Rationalizability in terms of outcomes when the restrictions correspond to belief in a distribution over terminal nodes. Moreover, under such restrictions, the epistemic priority between rationality and belief restrictions is irrelevant for the predicted outcomes.
We develop a product-differentiated model where the product space is a network defined as a set of varieties (nodes) linked by their degrees of substitutability (edges). We also locate consumers into this network, so that the location of each consumer (node) corresponds to her "ideal" variety. We show that there exists a unique Bertrand-Nash equilibrium where prices are determined by both the firms' sign-alternating Bonacich centralities and the average willingness to pay across consumers. We also investigate how local product differentiation and the spatial discount factor affect the equilibrium prices. We show that these effects non-trivially depend on the network structure. In particular, we find that, in a star-shaped network, the central firm does not always enjoy higher monopoly power than the peripheral firms.
At the beginning of a dynamic game, players may have exogenous theories about how the opponents will play. If these theories are commonly known, players will refine their first-order beliefs and challenge their own theories through strategic reasoning. I propose a new solution concept, Selective Rationalizability, which captures the following hypothesis: when the observed behavior is not compatible with the beliefs in rationality and in the theories of all orders, players keep the beliefs in rationality that are compatible with the observed behavior, and drop the incompatible beliefs in the theories. Thus, Selective Rationalizability captures Common Strong Belief in Rationality (Battigalli and Siniscalchi, 2002) and refines Extensive-Form Rationalizability (Pearce, 1984, Battigalli, 1996), whereas Strong-Δ-Rationalizability (Battigalli, 2003, Battigalli and Siniscalchi, 2003) captures the opposite epistemic priority choice. Selective Rationalizability is extended to encompass richer epistemic priority orderings among different theories of opponents' behavior. This allows to shed some new light on strategic stability (Kohlberg and Mertens, 1986).
When not all objects are acceptable to all agents, maximizing the number of objects actually assigned is an important design concern. We compute the guaranteed size ratio of the Probabilistic Serial mechanism, i.e., the worst ratio of the actual expected size to the maximal feasible size. It converges decreasingly to as the maximal size increases. It is the best ratio of any Envy-Free assignment mechanism.
Combinatorial Clock Auctions (CCAs) have recently been used around the world to allocate mobile telecom spectrum. CCAs are claimed to significantly reduce the scope for strategic bidding. This paper shows, however, that bidding truthfully does not constitute an equilibrium if bidders also have an incentive to engage in spiteful bidding to raise rivals' cost. The restrictions on further bids imposed by the clock phase of a CCA give certainty to bidders that certain bids above value cannot be winning bids, assisting bidders to engage in spiteful bidding.
Economic predictions often hinge on two intuitive premises: agents rule out the possibility of others choosing unreasonable strategies (‘strategic reasoning’), and prefer strategies that hedge against unexpected behavior (‘cautiousness’). These two premises conflict and this undermines the compatibility of usual economic predictions with reasoning-based foundations. This paper proposes a new take on this classical tension by interpreting cautiousness as robustness to ambiguity. We formalize this via a model of incomplete preferences, where (i) each player's strategic uncertainty is represented by a possibly non-singleton set of beliefs and a (ii) rational player chooses a strategy that is a best-reply to every belief in this set. We show that the interplay between these two features precludes the conflict between strategic reasoning and cautiousness and therefore solves the inclusion-exclusion problem raised by Samuelson (1992). Notably, our approach provides a simple foundation for the iterated elimination of weakly dominated strategies.
In this paper we introduce and analyze the procedural egalitarian solution for transferable utility games. This new concept is based on the result of a coalitional bargaining procedure in which egalitarian considerations play a central role. The procedural egalitarian solution is the first single-valued solution which coincides with the constrained egalitarian solution of Dutta and Ray (1989) on the class of convex games and which exists for any TU-game.
We provide epistemic foundations for permissibility (Brandenburger, 1992), a strategic-form solution concept for finite games which coincides with the Dekel-Fudenberg procedure, i.e., the elimination of all weakly dominated strategies, followed by the iterated elimination of strictly dominated strategies. We show that permissibility characterizes the behavioral implications of “cautious rationality and common weak belief of cautious rationality” in the canonical, universal type structure for lexicographic beliefs. For arbitrary type structures, we show that the behavioral implications of these epistemic assumptions are characterized by the solution concept of full weak best response set, a weak dominance analogue of best response set (Pearce, 1984).