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Abstract:
This paper assumes that groups of consumers in network markets can coordinate their choices when it is in their best interest to do so, and when coordination does not require communication. It is shown that multiple asymmetric networks can coexist in equilibrium if consumers have heterogeneous reservation values. A monopolist provider might choose to operate multiple networks to price differentiate consumers on both sides of the market. Competing network providers might operate networks such that one of them targets high reservation value consumers on one side of the market, while the other targets high reservation value consumers on the other side. Firms can obtain positive profits in price competition. In these asymmetric equilibria product differentiation is endogenized by the network choices of consumers. Heterogeneity of consumers is necessary for the existence of this type of equilibrium.

Coalitional agreements, coordination, network externalities, optimal pricing, platform competition, price discrimination, two-sided markets

Abstract:
This paper analyzes pricing decisions and competition in network markets, assuming that groups of consumers can coordinate their choices when it is in their interest, if coordination does not require communication. It is shown that multiple asymmetric networks can coexist in equilibrium. A monopolist might operate multiple ex ante identical networks to price differentiate. In Bertrand competition different firms might target high reservation value consumers on different sides of the market. Firms can obtain positive profits in price competition. Product differentiation in equilibrium is endogenized by consumers' network choices. Enough heterogeneity in reservation values is necessary for existence of these asymmetric equilibria.

two-sided markets, network externalities, platform competition, coordination

Abstract:
To facilitate systematic study of multi-self decision making, this paper proposes an axiomatic framework that encompasses a variety of models proposed in economics, psychology, and marketing. We model a decision-maker as a collection of utility functions (selves) and an aggregation rule (a theory of how selves are activated by choice sets) satisfying five simple axioms of social choice. For a broad class of aggregators, we show that with sufficiently many selves the resulting model can rationalize any choice function. We propose a method for counting IIA violations in a choice behavior, and show that the set of behaviors an aggregator can rationalize using n selves is bounded below by the set of choice functions for which the number of IIA violations is at most a given linear function of n. We apply our results to study Strotzian choice over menus and household decision-making.

Multiple selves, IIA violations, Rationalizability, Complexity

Abstract:
This paper proposes a theory of cooperation over finite horizons, focusing on public good contribution games, that implies the broadly documented feature of decreasing cooperation over time. The central assumption is that there are two types of players: those who only care about their own material payoffs, and those who reciprocate others' contributions. The main result is that if reciprocity functions satisfy some regularity conditions, then generically there is a unique perfect equilibrium, in which contributions are decreasing. In this equilibrium, selfish players contribute to induce subsequent contributions by reciprocal players, and this incentive diminishes as the end of the play approaches. The model explains the puzzling restart effect and is consistent with various other empirical findings. In one-shot games, the model predicts no contributions.

We also report the results of a series of experiments, using a probabilistic continuation design in which after each round, the game is restarted with low probability. The results support the implications of our model that the restart effect is present even with experienced players, whereas, in one-shot games, contributions disappear with experience. We show that experienced players correctly foresee the pattern of contributions, suggesting that the declining pattern comes from equilibrium play. We also identify the presence of conditional reciprocity among experienced players, and document that selfish players (identified exogenously) stop contributing earlier than reciprocal players, as implied by the model.