Joseph E. Harrington

Collusion among asymmetric firms: The case of different discount factors

Abstract This study investigates collusive behavior among asymmetric firms. For this purpose, we develop a selection criterion for deriving a unique collusive outcome and apply it to the case when firms have different discount factors. Our analysis reveals that for collusion to be self-enforcing, it is unnecessary that all firms have sufficiently high discount factors but rather only that firms, on average, have a sufficiently long-run view. The optimal collusive outcome entails a strict ordering of output quotas in which firms with relatively low discount factors receive a disproportionate share of market demand. As found in the case of a common discount factor, a fall in a firms discount factor reduces the likelihood of successful collusion. This effect reduces firm profits. On the other hand, in the event that firms can collude, a lowering of a firms discount factor increases its output quota so that its profits rise.

The role of party reputation in the formation of policy

Abstract This paper shows that a party can credibly establish a platform more moderate than the ideology of its members and thereby raise the probability that the partys nominee wins the election. A lame duck incumbent optimally implements his partys platform in order to maintain his partys reputation for having a moderate platform. This increases the likelihood that his party retains power. When candidates credibly locate themselves in policy space via this mechanism, we show that if candidates are sufficiently impatient, then their policies are bounded away from one another. The policy convergence result is not robust.

Cartel Pricing Dynamics with Cost Variability and Endogenous Buyer Detection

Abstract This paper characterizes collusive pricing patterns when buyers may detect the presence of a cartel. Buyers are assumed to become suspicious when observed prices are anomalous. We find that the cartel price path is comprised of two phases. During the transitional phase, price is generally rising and relatively unresponsive to cost shocks. During the stationary phase, price responds to cost but is much less sensitive than under non-collusion or simple monopoly; a low price variance may then be a collusive marker. Compared to when firms do not collude, cost shocks take a longer time to pass-through to price.

A re-evaluation of perfect competition as the solution to the Bertrand price game

Abstract On the basis that it is the unique Nash equilibrium, the perfectly competitive outcome is well accepted as the solution to the Bertrand price game. We apply a more restrictive solution concept than Nash equilibrium and find that perfect competition is not a reasonable outcome. Of course, a perfect equilibrium exists for all finite games so that a reasonable outcome certainly exists for the Bertrand price game if strategy sets are restricted to be finite. Investigation into the finite strategy set version reveals two interesting results. First, while a unique reasonable outcome exists for the finite game, it is not perfectly competitive though it is approximately competitive when strategy sets are sufficiently fine. Second, the Bertrand price game is found to be degenerate in the sense that it is a member of a set of measure zero of finite games for which it is not true that an odd and finite number of Nash equilibria exist.

Collusion and predation under (almost) free entry

Abstract This study investigates the degree of cooperation that firms can support in the absence of significant barriers to entry. A Free-Entry Subgame Perfect Equilibrium is defined by (q,n), where q is the collusive output rate and n is the number of active firms, such that there is no incentive for an active firm to deviate output from q and there is no incentive for a potential entrant to enter the industry. It is shown that for all n⩾1, if the discount factor is sufficiently high there exists a free-entry equilibrium in which active firms sustain a non-trivial degree of cooperation. Cooperation is supported by active firms credibly threatening to respond to entry with a period of aggressive competition.

The advantageous nature of risk aversion in a three-player bargaining game where acceptance of a proposal requires a simple majority

Abstract In a three-player bargaining game in which acceptance of a proposed allocation requires only the approval of a simple majority, it is shown that the most (least) risk averse player receives the highest (lowest) expected share when the preferences of the players are not too diverse.

Some implications of antitrust laws for cartel pricing

Abstract Price dynamics are characterized for a price-fixing cartel. Antitrust laws reduce cartel prices even though cartel detection occurs with probability zero. In response to cheating, the non-collusive price gradually moves from the collusive price to the static Nash equilibrium price.

The joint profit maximum as a free-entry equilibrium outcome

Abstract This study investigates the degree of collusion that can be sustained at a free-entry equilibrium. When the number of active firms is endogenous, an increase in the discount factor is found to have two counter-acting effects on the incentive for active firms to deviate from the collusive arrangement. Holding the number of firms fixed, a higher discount factor reduces the incentive for cheating according to the standard argument. However, a higher discount factor also makes entry more profitable since entry entails an initial loss (the cost of entry) and a future stream of positive profits. Raising the discount factor then increases the number of active firms which tends to increase the incentive for firms to cheat. Our analysis shows that the first effect dominates so that the joint profit maximum can be sustained as a free-entry equilibrium outcome when the discount factor is sufficiently high.

A non-cooperative bargaining game with risk averse players and an uncertain finite horizon

Abstract For an alternating offer bargaining game with an uncertain horizon, the equilibrium payoff to a player is greater, the less risk averse is he relative to his opponent. As the horizon becomes infinite in length, the equilibrium partition converges to the Nash bargaining solution.

Modelling the role of information in elections

A foundational issue concerning elections is the incentives for candidates to provide informative and truthful campaign messages with regards to their policy intentions. The standard model of electoral competition formulated by Hotelling [1929] and Downs [1957] is incapable of addressing this issue because of the ad hoc assumption that the winning candidate must fulfill his campaign promises. Using recent developments in games of incomplete information, this paper develops a model of electoral competition for the purpose of investigating the role of information in elections.