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This paper departs from the standard profit-maximizing model of firm behavior by assuming that firms are motivated in part by personal animosity–or respect–towards their competitors. A reciprocal firm responds to unkind behavior of rivals with unkind actions (negative reciprocity), while at the same time, it responds to kind behavior of rivals with kind actions (positive reciprocity). We find that collusion is easier to sustain when firms have a concern for reciprocity towards competing firms provided that they consider collusive prices to be kind and punishment prices to be unkind. Thus, reciprocity concerns among firms can have adverse welfare consequences for consumers.

The assumption that individuals behave as if maximizing their material payoffs, despite its central role in economic analysis, is at odds with a large body of evidence from psychology and from experimental economics. Economic agents often pursue objectives other than actual payoff maximization. Many observed departures from material payoff maximizing behavior arise through actions that favor fairness or reciprocity.

Fairness and reciprocity have been shown to explain behavior in bargaining games and in trust games. For example, in ultimatum games offers are usually much more generous than predicted by subgame perfect equilibrium and low offers are often rejected. These offers are consistent with an equilibrium in which proposers make offers knowing that responders may reject allocations that appear unfair.

The same effect is observed in markets. [

The impact of fairness and reciprocity on market outcomes is an active area of research. [

In this paper we ask whether reciprocity may help to sustain collusive behavior. For instance, if a collusive agreement is seen by the parties as a kind outcome, then if one party reneges on the agreement and undercuts the price (or boosts its output), its rivals may be offended and hence punish the deviator aggressively (even at extra cost to themselves). Thus, because negative reciprocity induces more aggressive punishments for deviating, it could help sustain collusion relative to situations in which firms care only about their own profits.

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To model reciprocity we follow [

In a standard setting, collusion can be sustained as an equilibrium by self-interested players if they interact infinitely often and are sufficiently patient. A player is said to be patient if his discount factor is sufficiently close to one. In order to determine whether collusion is or is not facilitated by reciprocity we compare the minimal discount factor that allows the same collusive outcome to be sustained when players are reciprocal and when they are self-interested.

We find that reciprocity facilitates collusion under dynamic price competition if players consider collusive prices to be kind and punishment prices to be unkind. This happens because the future losses of deviating from collusion are higher for reciprocal players than for self-interested ones and the short-run deviation gain of a reciprocal player is less than the short-run deviation gain of a self-interested one. The intuition behind this result is as follows.

If players expect the collusive prices to be played and consider those prices to be kind, then collusion is a positive reciprocity state,

If a player considers the collusive prices of the rivals as kind, then when he deviates from collusion he attains a lower monetary payoff than a self-interested player because he cares about the monetary payoffs of his rivals and so he is less willing to undercut the collusive price. Additionally, when a reciprocal player deviates from collusion he suffers a loss in fairness payoffs because he lowers the monetary payoffs of his rivals. These two effects imply that the short-run deviation gain of a reciprocal player is less than the short-run deviation gain of a self-interested one.

Our paper is an additional contribution to the literature on the factors that help or hinder collusion. It is now well known that concentration, barriers to entry, cross-ownership, symmetry and multi-market contracts facilitate collusion–see [

The main policy implication of our paper is that if firms have reciprocal preferences this can have adverse welfare consequences for consumers. In contrast, [

The rest of the paper proceeds as follows.

The existing theories of social preferences can be classified into three broad categories. The first one is the distributional preference approach where social preferences only depend on the distribution of material payoffs. This includes [

The second category consists of intention-based models and includes [

The third category explores the axiomatic foundations that generate utility functions that display social preferences. [

We apply [

The first term on the right-hand side of (1) is the monetary payoff of player

In this section we analyze how fairness and reciprocity change the outcome of static price competition. Let

We denote the Nash equilibrium price of a self-interested player

Our first results compares the Nash equilibrium prices in

This result characterizes the impact of fairness and reciprocity on equilibrium prices under static price competition. The intuition behind Proposition 1 is as follows: when players expect their rivals to set kind prices they place a positive weight on the monetary payoffs of the rivals,

To analyze the impact of fairness and reciprocity on the Nash equilibrium payoffs we focus on the symmetric case of

Proposition 2 part (i) says that if reciprocal players expect their rivals to set kind prices, then they attain a higher equilibrium payoff than that obtained by self-interested players. This happens because reciprocal players will choose higher equilibrium prices than self-interested players. This increases reciprocal players’ monetary payoffs and, in addition, leads to fairness payoff gains due to the rivals’ kind behavior. In contrast, Proposition 2 part (ii) says that if reciprocal players expect their rivals to set unkind prices, then they attain a lower equilibrium payoff than that obtained by self-interested players. This happens because reciprocal players will choose lower equilibrium prices than self-interested players. This lowers reciprocal players’ monetary payoffs and, in addition, leads to fairness payoff losses due to the rivals’ unkind behavior.

In this section we study the impact of fairness and reciprocity on collusion using a dynamic price competition set-up. More precisely, the symmetric static price games described in the previous section will be played over an infinite horizon. Let

Players are able to sustain a collusive outcome when the payoff from collusion is no less than the payoff from deviation. To understand how fairness and reciprocity influence collusion we compare the incentives to cooperate of self-interested players in

The standard approach to study collusion in infinitely repeated games assumes that players use grim trigger strategies to punish any deviation from collusion,

The same reasoning applies when players have reciprocal preferences. A reciprocal player

We say that fairness and reciprocity facilitate collusion when the collusive price profile can be sustained at a lower critical discount factor when players are reciprocal than when they are self-interested. If the opposite happens we say that fairness and reciprocity make collusion harder.

We are now ready to state the main result of the paper.

This result provides sufficient conditions for collusion to be easier to sustain in the infinitely repeated price game with reciprocal players than in the infinitely repeated price game with self-interested players.

If collusion is a positive reciprocity state and the punishment phase is a negative reciprocity state,

If collusion is a positive reciprocity state,

Proposition 3 follows from two critical assumptions. First, the assumption that players place a positive weight on the monetary payoffs of the rivals when they expect them to play the collusive prices,

To better illustrate the intuition behind Proposition 3 consider the two prisoners’ dilemma (PD) games.

Each player has the choice between cooperate,

A reciprocal player who expects the rival to cooperate places weight

A reciprocal player who expects the rival to defect places weight

Cooperation is a strictly dominated strategy in the PD game with reciprocal players if

Now suppose the two PD games are played an infinite number of times and that players discount the future at rate

A sufficient condition for (8) to hold is

In this section we present an example that illustrates our results. Two identical firms operate in the market, selling possibly differentiated final products. Each firm faces the following inverse demand function (see [

The static payoff of a reciprocal player is given by

The best-response function of a reciprocal player is

Let us now consider how reciprocity affects collusion. The collusive prices are the solution to

This paper contributes to the literature on the effect of fairness and reciprocity on market outcomes. Most of this literature has focused on the impact of fairness concerns by consumers on welfare. Here we focus on the role fairness and reciprocity play for firms’ incentives to collude.

We depart from the standard model of firm behavior by assuming that firms are motivated in part by personal animosity–or respect–towards a rival. Hence, firms might punish rivals who behave “unfairly” towards them and reward rivals who behave “fairly.”

We find that collusion is easier to sustain when firms have a concern for reciprocity towards competing firms provided that they consider collusive prices to be kind and punishment prices to be unkind.

Our results hold provided certain conditions are met. For example, we rule out fairness concerns on the part of consumers. This assumption was made on methodological grounds, to better isolate the effect of fairness and reciprocity among firms on collusive outcomes.

We also rule out that firms have fairness considerations with respect to consumers. Contrary to this assumption, [

We study the impact of fairness and reciprocity on collusion when players use Nash reversion to punish deviations. [

We gratefully acknowledge comments from Matthew Rabin, Joel Sobel, and seminar audiences at University of Copenhagen, University of Cergy-Pontoise, Free University of Amsterdam, University of Geneva, and University of Lausanne. Doruk İriş thanks the support of the Sogang University Research Grant of 2012.

(ii) Suppose, by contradiction, that

(i) We know from Proposition 1 part (i) that if

(ii) Note that if

We start by showing that if

Hence, (27) and (28) hold strictly when

We assume that the weight player

This assumption implies that mutual cooperation yields a higher payoff to a reciprocal player than to self-interested one since

If a reciprocal player considers

Condition (

The results in this section would also hold for quantity competition with quantitites as strategic substitutes, the dual of price competition with prices as strategic complements. Reciprocity facilitates collusion under quantity competition when each player places a strictly positive weight on the monetary payoff of a rival who produces the collusive output and a nonpositive weight on the monetary payoff of a rival who produces the Nash output. The intuition behind this result is similar to that behind Proposition 3.

A sufficient condition for (20) to be satisfied is that