To facilitate systematic study of multi-self (or group) decision making, this paper proposes a framework that encompasses a variety of models proposed in economics, psychology, and marketing. We model choice as arising from the aggregation of a collection of utility functions. We propose a method for characterizing the extent of irrationality of a choice behavior, and use this measure to provide a lower bound on the set of choice behaviors that can be rationalized with n utility functions. Within a class of models, generically at most five “reasons” are needed for every “mistake.”
We investigate situations in which agents can only communicate to each other through a chain of intermediators, for example because they have to obey institutionalized communication protocols. We assume that all involved in the communication are strategic, and might want to influence the action taken by the final receiver. The set of pure strategy equilibrium outcomes is simple to characterize, monotonic in each intermediator’s bias, does not depend on the order of intermediators, and intermediation in these equilibria cannot improve information transmission. However, none of these conclusions hold for mixed equilibria. We provide a partial characterization of mixed equilibria, and offer an economically relevant sufficient condition for every equilibrium to be outcome-equivalent to a pure equilibrium and hence the simple characterization and comparative statics results hold for the set of all equilibria.
This paper contributes to understanding the role of interest groups in legislative decision-making, and offers an explanation to two widely discussed puzzles concerning the legislative process: why legislative bodies sometimes tie their own hands by delegating power to specialized committees, and why committees consist of preference outliers. In our model, the legislature has to collect information from a strategic lobbyist. Depending on the lobbyist’s bias, the legislature either wants to delegate power to a committee aligned with the lobbyist, or retain power but communicate with the lobbyist through an adversely biased committee.
We show that in multi-sender cheap talk games, if the state space is large enough, then there exist equilibria arbitrarily close to full revelation of the state that are robust to introducing imperfections in the senders’ observations. The result implies that even when only equilibria robust to noise are considered, if there are multiple experts to consult with and the state space is large, there is a communication equilibrium that is strictly better for the principal than delegating the decision right to one of the experts.
Institutional rules provide natural deadlines for negotiations in legislative bargaining. In the continuous-time bargaining model framework of Ambrus and Lu (2010) we show that as the time horizon of the bargaining increases, equilibrium payoffs with deadline converge to stationary equilibrium payoffs of the infinite-horizon bargaining game. We provide a characterization of these limit payoffs, and show that under a K-majority rule, the payoffs of the K legislators with the lowest relative recognition probabilities have to be equal to each other. Hence, by varying recognition probabilities, possible limit equilibrium payoffs are constrained to a lower-dimensional subset of the set of all possible allocations. This contrasts with the result of Kalandrakis (2006) that in the infinite-horizon Baron and Ferejohn (1989) framework, for any discount factor, any division of the surplus can be achieved as a stationary equilibrium payoff through some choice of recognition probabilities.
This paper uses ransom prices and time to ransom for over 10,000 captives rescued from the Barbary Corsairs to investigate the empirical relevance of dynamic bargaining models with one-sided asymmetric information. Our dataset includes information that only the buyer knew. In addition, we observe multiple negotiations that were ex ante similar from the uninformed party's (seller's) point of view. Empirical results are consistent with many of the theoretical predictions of dynamic bargaining models. In particular, variation in bargaining costs helps explain the observed differences in negotiation outcomes between different locations.
We propose a finite-horizon continuous-time framework for coalitional bargaining that has the following features: (i) Expected payoffs in Markov-perfect equilibrium (MPE) are unique, generating sharp predictions and facilitating comparative statics investigations; (ii) MPE are the only subgame-perfect Nash equilibria (SPNE) of the model that can be approximated by SPNE of nearby discrete-time bargaining models satisfying a genericity condition, providing justification for focusing on MPE in our model; (iii) The model is relatively tractable analytically. We investigate MPE payoffs as the time horizon goes to infinity. In convex games, we connect these limit payoffs to the core of the characteristic function underlying the bargaining game.
This paper shows that in online auctions like ebay, if bidders are not continuously participating in the auction but can only place bids at random times, then many different equilibria arise besides truthful bidding, despite the option to leave proxy bids. These equilibria can involve gradual bidding, periods of inactivity, and waiting to start bidding towards the end of the auction - bidding behaviors common on ebay. For symmetric bidders in a complete information setting, we characterize a class of equilibria that include the best and worst Markovian equilibria for the seller. In specific cases we also identify the worst non-Markovian equilibrium for the seller. The revenue of the seller in these equilibria can be a small fraction of what could be obtained at a sealed-bid second-price auction, and it can paradoxically decrease in the value of the object for the buyers. We show that the existence of equilibria with similar features extends to settings with asymmetric bidders, time-dependent arrival rates, and asymmetric information.
This paper experimentally investigates the effects of a costly punishment option on cooperation and social welfare in long finitely repeated public good contribution games. In a perfect monitoring environment increasing the severity of the potential punishment monotonically increases both contributions and the average net payoffs of subjects. In a more realistic imperfect monitoring environment, we find a U-shaped relationship between the severity of punishment and average net payoffs. Access to a standard punishment technology in this setting significantly decreases net payoffs, even in the long run. Access to a very severe punishment technology leads to roughly the same payoffs as with no punishment option, as the benefits of increased cooperation exactly offset the social costs of punishing. Our findings parallel findings in the empirical literature on gun control in that more severe weapons in criminal acts and in self-defense are used less frequently, as their intimidating factor is often sufficient in preventing offenses.
We develop a model of informal risk-sharing in social networks, where relationships between individuals can be used as social collateral to enforce insurance payments. We characterize incentive compatible risk-sharing arrangements and obtain two results. (1) The degree of informal insurance is governed by the expansiveness of the network, measured by the number of connections that groups of agents have with the rest of the community, relative to group size. Two-dimensional networks, where people have connections in multiple directions, are sufficiently expansive to allow very good risk-sharing. We show that social networks in Peruvian villages satisfy this dimensionality property; thus, our model can explain Townsend's (1994) puzzling observation that village communities often exhibit close to full insurance. (2) In second-best arrangements, agents organize in endogenous "risk-sharing islands" in the network, where shocks are shared fully within, but imperfectly across islands. As a result, network based risk-sharing is local: socially closer agents insure each other more.
This paper shows that the presence of different types of players - those who only care about their own material payoffs and those who reciprocate others' contributions - can explain the robust features of observed contribution patterns in public good contribution games, even without the presence of asymmetric information. We show what conditions on reciprocity are sufficient for a unique perfect equilibrium, in which contributions are decreasing. Under these conditions, selfish players have enough future benefits to induce subsequent contributions by reciprocal players, and this incentive diminishes as the end of the game approaches. The model explains the puzzling restart effect and is consistent with various other empirical findings. We also report the results of a series of experiments, using a probabilistic continuation design in which after each set of 10-period games, the group is restarted with low probability. We find specic support for the theory in our data, including that selfish players (identied exogenously) stop contributing earlier than reciprocal players, as directly implied by the model.
Existing theoretical and empirical research on dowries has difficulty accounting for the large changes in dowry levels observed in many countries over the past few decades. To explain trends in dowry levels in Bangladesh, we draw attention to an institutional feature of marriage contracts previously ignored in the literature: the mehr or traditional Islamic brideprice, which functions as a prenuptial agreement in Bangladesh due to the default practice of being only payable upon divorce. We develop a model of marriage contracts in which mehr serves as a barrier to husbands exiting marriage and a component of dowry is an amount that ex ante compensates the groom for the cost of mehr. The contracts are welfare-improving because they induce husbands to internalize the social costs of divorce for women. We investigate how mehr and dowry respond to exogenous changes in the costs of polygamy and divorce, and show that our model gives a different set of predictions than traditional models of dowry payments without contractible mehr. To test the model’s predictions empirically, we use data collected on marriage contracts between 1956 and 2004 from a large household survey from the Northwest region of the country, and make use of key changes in Muslim Family Law in 1961 and 1974. We show that major changes in dowry levels took place precisely after the legal changes, corresponding to simultaneous changes in levels of mehr.
We revisit the phenomenon that group decisions differ systematically from decisions of individuals. Our experiment solicits individual and group decisions from the same subjects in two settings, gift-exchange games and lottery choices. With no deliberation and voting, the group decision is determined by the median individual decision, without a shift. With deliberation but no imposed decision rule, the individual one position towards the selfish direction also becomes influential. In lottery choices we find no group shift relative to the median. We demonstrate that the standard practice of comparing means of group and individual decisions would incorrectly identify a level shift.
This paper investigates the problem of delegating decision-making when there are limitations on using monetary transfers to provide incentives, but the principal can prescribe costly activities such as bureaucratic paperwork on the agent for choosing certain actions. For simplicity, we assume that these activities are purely wasteful, and refer to them as money burning. Through the agent’s ex-ante participation constraint, the use of money burning is costly for the principal. Despite this, the optimal delegation contract can involve money burning, both when contingent monetary transfers are not possible, and when payments from the principal to the agent are bounded from below. We show that under certain regularity conditions the optimal contract in case of a positively biased agent imposes zero money burning in low states, money burning is increasing in the state, and the implemented action is always between the ideal points of the participants. If both transfers and monetary transfers are allowed, whether the optimal contract involves money burning depends on how important the action choice for the principal relative to the agent in monetary terms, and on the outside option of the agent relative to the minimal transfer. If the outside option of the agent is high enough, the optimal contract is efficient, and there is no money burning. If the outside option is low enough, there is money burning in almost all states. For an intermediate region of parameters, monetary transfers (positive incentives) are used in low states, while money burning (negative incentives) are used in high states. The results point out a distortionary effect of minimum wages not discussed in the literature: increasing the minimum wage makes it more likely that employers switch to socially inefficient nonmonetary incentives from financial ones.
This paper investigates firms’ pricing decisions and consumers’ network choices in two-sided markets with network externalities. Consumers are heterogeneous in how much they value the externality. We show that imposing some restrictions on the extent of coordination failure among consumers leads to clear qualitative conclusions about equilibrium market configurations. Multiple asymmetric networks can coexist in equilibrium, both in the case of a monopolist network provider and in the case of competing providers. These equilibria have the property that can be observed in many different two-sided markets: one network is cheaper and larger on one side, while the other network is cheaper and larger on the other side. Product differentiation is endogenized by consumers’ network choices.
This paper generalizes the concept of best response to coalitions of players and offers epistemic definitions of coalitional rationalizability in normal form games. The (best) response of a coalition is defined to be an operator from sets of conjectures to sets of strategies. A strategy is epistemic coalitionally rationalizable if it is consistent with rationality and common certainty that every coalition is rational. A characterization of this solution set is provided for operators satisfying four basic properties. Special attention is devoted to an operator that leads to a solution concept that is generically equivalent to the iteratively defined concept of coalitional rationalizability.
Dispersion in retail prices of identical goods is inconsistent with the standard model of price competition among identical firms, which predicts that all prices will be driven down to cost. One common explanation for such dispersion is the use of a loss-leader strategy, in which a firm prices one good below cost in order to attract a higher customer volume for profitable goods. By assuming each consumer is forced to buy all desired goods at a single firm, we create the possibility of an effective loss-leader strategy. We find that such a strategy cannot occur in equilibrium if individual demands are inelastic, or if demands are diversely distributed. We further show that equilibrium loss-leaders can occur (and can result in positive profits) if there are demand complementarities, but only with delicate relationships among the preferences of all consumers.
This paper provides empirical evidence of the influence of adolescent marriage opportunities on female schooling attainment and gives predictions of the impact for imposing universal age-of-consent laws. Using data from rural Bangladesh, we explore the commonly cited hypotheses that women attain less schooling as a result of social and financial pressure to marry young. We isolate the causal effect of marriage timing by exploiting variation in the timing of menarche as an instrumental variable for age of first marriage. Our results indicate that marriage age matters: Each additional year that marriage is delayed is associated with 0.22 additional years of schooling attainment and 5.6% higher probability of literacy. Delayed marriage is also associated with a significant increase in use of preventive health care services, some of which appears to be independent of the change in schooling, indicating separate “age effects” of delaying marriage. In the context of competitive marriage markets we show that the above results can be used to obtain estimates of the change in equilibrium female education that would arise from introducing a minimum legal age of marriage. The resulting analysis implies that, under reasonable assumptions, enforcing universal age of consent laws would have a strong positive impact on female schooling.
This paper analyzes multi-sender cheap talk when the state space might be restricted, either because the policy space is restricted, or the set of rationalizable policies of the receiver is not the whole space. We provide a necessary and sufficient condition for the existence of a fully revealing perfect Bayesian equilibrium for any state space. We show that if biases are large enough and are not of similar directions, where the notion of similarity depends on the shape of the state space, then there is no fully revealing perfect Bayesian equilibrium. The results suggest that boundedness, as opposed to dimensionality, of the state space plays an important role in determining the qualitative implications of a cheap talk model. We also investigate equilibria that satisfy a robustness property, diagonal continuity.
This paper investigates competition for advertisers in media markets when viewers can subscribe to multiple channels. A central feature of the model is that channels are monopolists in selling advertising opportunities toward their exclusive viewers, but they can only obtain a competitive price for advertising opportunities to multi-homing viewers. Strategic incentives of firms in this setting are different than those in former models of media markets. If viewers can only watch one channel, then firms compete for marginal consumers by reducing the amount of advertising on their channels. In our model, channels have an incentive to increase levels of advertising, in order to reduce the overlap in viewership. We take an account of the differences between the predictions of the two types of models and find that our model is more consistent with recent developments in broadcasting markets. We also show that if channels can charge subscription fees on viewers, then symmetric firms can end up in an asymmetric equilibrium in which one collects all or most of its revenues from advertisers, while the other channel collects most of its revenues via viewer fees.