The folk theorem for repeated games with observation costs

This paper studies repeated games with private monitoring where players make optimal decisions with respect to costly monitoring activities, just as they do with respect to stage-game actions. We consider the case where each player can observe other players' current-period actions accurately only if he incurs a certain level of disutility. In every period, players decide whether to monitor other players and whom to monitor. We show that the folk theorem holds for any finite stage game that satisfies the standard full dimensionality condition and for any level of observation costs. The theorem also holds under general structures of costless private signals and does not require explicit communication among the players. Therefore, tacit collusion can attain efficient outcomes in general repeated games with private monitoring if perfect private monitoring is merely feasible, however costly it may be

Optimal Sharing Rules in Repeated Partnerships

We study a simple model of repeated partnerships with noisy outcomes. Two partners first choose a sharing rule, under which they start their repeated interaction. We characterize the sharing rule which supports the most efficient equilibrium, and show that it suffices to consider two particular sharing rules. One is an asymmetric sharing rule, which induces only a more productive partner to work. It is optimal for impatient or less productive partners. The other treats them more evenly, and prevails for more productive and patient partners. Those results indicate how technological parameters and patience determine the role of a more productive partner. If the partners become more productive or more patient, the productive partner ceases to be a residual claimant and sacrifices his own share, in order to foster teamwork.

Switching Costs in Infinitely Repeated Games

We show that small switching costs can have surprisingly dramatic effects in infinitely repeated games if these costs are large relative to payoffs in a single period. This shows that the results in Lipman and Wang [2000] do have analogs in the case of infinitely repeated games. We also discuss whether the results here or those in Lipman and Wang [2000] imply a discontinuity in the equilibrium outcome correspondence with respect to small switching costs. We conclude that there is not a discontinuity with respect to switching costs but that the switching costs do create a discontinuity with respect to the length of a period.infinite horizon, repeated games, switching costs, Folk Theorem

"Repeated Games, Entry in The New Palgrave Dictionary of Economics, 2nd Edition"

This entry shows why self-interested agents manage to cooperate in a long-term relationship. When agents interact only once, they often have an incentive to deviate from cooperation. In a repeated interaction, however, any mutually beneficial outcome can be sustained in an equilibrium. This fact, known as the folk theorem, is explained under various information structures. This entry also compares repeated games with other means to achieve efficiency and briefly discuss the scope for potential applications.

Communication in Dynastic Repeated Games: `Whitewashes' and `Coverups

We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication. When communication is costless and messages are sent simultaneously, communication mechanisms or protocols exist that sustain the same set of equilibrium payoffs as in the standard repeated game. When communication is costless but sequential, the incentives to `whitewash' the unobservable past history of play become pervasive. These incentives to whitewash can only be countered if some player serves as a `neutral historian' who verifies the truthfulness of others' reports while remaining indifferent in the process. By contrast, when communication is sequential and (lexicographically) costly, all protocols admit only equilibria that sustain stage Nash equilibrium payoffs. We also analyze a centralized communication protocol in which history leaves a `footprint' that can only hidden by the current cohort by a unanimous `coverup'. We show that in this case only weakly renegotiation proof payoffs are sustainable in equilibrium.Dynastic Repeated Games, Communication, Whitewashing, Coverups

Making Sense of Non-Binding Retail-Price Recommendations

This paper provides a theoretical rationale for non-binding retail price recommendations (RPRs) in vertical supply relations. Analyzing a bilateral manufacturer-retailer relationship with repeated trade, we show that linear relational contracts can implement the surplusmaximizing outcome. If the manufacturer has private information about production costs or consumer demand, RPRs may serve as a communication device from manufacturer to retailer. We characterize the properties of efficient bilateral relational contracts with RPRs and discuss extensions to settings where consumer demand is affected by RPRs, and where there are multiple retailers or competing supply chains.vertical relationships, relational contracts, asymmetric information, price recommendations

Making Sense of Non-Binding Retail-Price Recommendations

We model non-binding retail-price recommendations (RPRs) as a communication device facilitating coordination in vertical supply relations. Assuming both repeated vertical trade and asymmetric information about production costs, we show that RPRs may be part of a relational contract, communicating private information from manufacturer to retailer that is indispensable for maximizing joint surplus. We show that this contract is self-enforcing if the retailer’s profit is independent of production costs and punishment strategies are chosen appropriately. We also extend our analysis to settings where consumer demand is variable or depends directly on the manufacturer’s RPRs.vertical relationships, relational contracts, asymmetric information, price recommendations