“Group consumption, free-riding, & informal reciprocity agreements”. Why do people use informal reciprocity agreements? Most analysis answers this question by invoking the importance of social capital Social capital – two important components - networks - norms - reciprocity is a critical norm that develops trust How do we get good networks and good norms? How are they generated and sustained? - remember that not all types of social capital are “good” One tool for analyzing networks and norms is the infinitely repeated Prisoner’s dilemma - equilibrium analysis is better at answering how to sustain social capital than at answering how the equilibrium is generated in the first place

Motivation - Main Results. Groups of consumers can share expenses without using a formal club or a price system - Informal reciprocity agreements are important for explaining how this occurs What are the conditions under which group consumption is likely to involve informal reciprocity agreements rather than a price system? Main Results: The formal model shows that reciprocity agreements are used when: 1) transaction costs are high 2) the good is inexpensive 3) demand is inelastic 4) the group continues to interact over time 5) the consumers are patient 6) the time between interactions is short 7) the group is small and homogeneous

Model. Focus on a group of consumers sharing a meal with two payment arrangements 1) each period, every customer pays their own bill 2) consumers take turns paying the bill under a tacit agreement -consumer i pays for everyone today and then gets n-1 free meals, and so on. n consumers dine together once each period (assume that everyone is identical) Three scenarios: 1) consumer dines alone, which is the benchmark for ostracism 2) consumers dine together, but each person pays his own bill (high transaction costs) 3) consumers dine together and use an informal reciprocity agreement. They take turns paying the whole bill (bill-sharing) Each time a consumer pays a bill he bears a transaction cost of c (inconvenience cost) - the main motivation for bill sharing is the transaction cost savings

Consumer Optimization. Additional variable in the utility function is group companionship In the 3 scenarios, 1)y O = outside group 2)y = inside group 3)y where y O.≤ y there is a cost to ostracism

Discounting.

Defection. Reciprocity assumption: - defection consists of not paying the bill when it is one’s turn to pay Defector punishment conditions (1)Renegotiation: if consumer i refuses to pay today, then consumer i can agree to pay next time (2)Ostracism: consumer i is kicked out of the group and eats alone forever If a player prefers bill sharing to deviating, the player must prefer paying the bill when it is his turn to both renegotiation and ostracism

Punishment Conditions.

Equilibrium Condition.

Multiple overlapping networks. If networks overlap then punishment in one network can help ensure cooperation in another network. Formal representation: Suppose that there are two ways for individuals in the group interact: - they eat lunch together and also work together. Suppose that at lunch they prefer bill-sharing to dining alone

Job Cooperation with Ostracism. Now suppose that the individuals in the group can also either cooperate or not on the job. Now suppose that non-cooperative behavior at work can be punished with ostracism from the lunch group. It may be the case that the threat of such ostracism is sufficient to ensure cooperation at work and have substantial effects on economic welfare Tying ensures cooperation at work if the following inequality holds:

Investments in Social Capital. How does cooperation emerge? In an infinitely repeated PD game, some equilibrium paths Pareto dominate others 1) equilibrium path {(C, C), (C, C),…, (C, C)} 2) equilibrium path {(D, D), (D, D),…, (D, D)} - path 1) Pareto dominates path 2) If players in the game start by defecting, how can we go from 2) to 1)? When consumers differ some maybe more willing to continue or begin an informal reciprocity agreement We can introduce investments into the repeated game analysis: - begin with no agreement - under what conditions is one likely to emerge? - one player has to be willing to cooperate and take a risk of being a sucker

Starting a reciprocity agreement. 2 players – no reciprocity agreement 2 types of people Joe will ask Mary to lunch if his expected lifetime payoff from asking is greater than his expected lifetime payoff from not asking

Beliefs.

Larger implications. The effect of n is tricky, since it has both a direct and an indirect effect Recall that the only decision is whether to pay bill - high n means paying the bill for more people, but a longer time before paying again. There may be many applications of the investing in social capital model For example, consider countries that currently do not cooperate in trade policies One country has to make an investment to encourage cooperation - many goods with different properties: price, cost, quantity, import tariffs. One county might initiate cooperation by lowering a tariff on some good. - which good? The results would be similar to the group consumption results