duopoly supergames with product differentiation abstract when goods are complements or very close substitutes more tacit collusion is supported by trigger strategies in price setting supergames than in quantity setting supergames for moderate or poor substitutes the situation is reversed this contrasts with the static situation where price setting strategies always lead to higher welfare

punishment strategies in repeated games evidence from experimental markets abstract an experiment is designed to provide a snapshot of the strategies used by players in a repeated price competition game with a random continuation rule one hundred pairs of subjects played the game over the internet with subjects having a few days to make their decisions in each round occasionally subjects are asked to enter one period ahead pricing strategies instead of prices according to the elicited strategies between 90 and 95 of subjects punish less harshly in their initial response to a deviation than implied by the grim trigger strategy and do so in a way that depends on the size of the other subject s deviation future earnings are highest for subjects adopting the tit for tat strategy even after controlling for a subject s past earnings punishment strategies are generally softer and more graduated than implied by a grim trigger strategy and do better as a result

price wars in price setting supergames this paper presents a method of generating price wars in price setting supergames the market is one where symmetric oligopolists produce a differentiated product and use price as a strategic variable prices are posted and can be observed by all there is thus little uncertainty or scope for secret price cutting nevertheless price wars occur they are precipitated by periodic but infrequent demand shocks firms use the wars to learn about changed conditions in the market so that they can calculate the new stationary nash equilibrium learning is modeled in a bayesian fashion via the kalman filter copyright 1989 by the london school of economics and political science

continuous reaction functions in duopolies abstract friedman and samuelson 1990 games econ behav 2 304 324 have recently shown that continuous reaction functions can support nontrivial outcomes as subgame perfect equilibria in repeated games this paper examines continuous reaction functions in duopolies we first establish a folk theorem showing that any feasible individually rational outcome in the stage game can be supported as a subgame perfect equilibrium outcome in continuous reaction functions given sufficiently high discount factors we then show that the set of discount factors for which outcomes can be supported by continuous reaction functions is at least as large as the corresponding sets under nash reversion trigger strategies and optimal two phase symmetric punishments the implication of these findings is that no generality in terms of possible equilibrium outcomes need be sacrificed in the course of requiring continuity journal of economic literature classification numbers d43 c72

interfirm rivalry in a repeated game an empirical test of tacit collusion rivalry in the vancouver retail gasoline market is modeled as a repeated game service station demand cost and intertemporal reaction functions are estimated from daily data on individual station prices costs and sales these functions are then used to calculate noncooperative and cooperative solutions to the constitutent game and the actual outcome of the repeated game the actual outcome is found to be substantially less lucrative than the monopoly solution nevertheless all stations are better off than if they played their noncooperative strategies in every period copyright 1987 by blackwell publishing ltd

rules communication and collusion narrative evidence from the sugar institute case detailed notes on weekly meetings of the sugar refining cartel show how communication helps firms collude and so highlight the deficiencies in the current formal theory of collusion the sugar institute did not fix prices or output prices were increased by homogenizing business practices to make price cutting more transparent meetings were used to interpret and adapt the agreement coordinate on jointly profitable actions ensure unilateral actions were not misconstrued as cheating and determine whether cheating had occurred in contrast to established theories cheating did occur but sparked only limited retaliation partly due to the contractual relations with selling agents jel l13 l41 this paper reexamines the cartel problem by studying the private discussions within one cartel while we find much that is in accord with george j stigler s 1964 basic insight that firms would structure an agreement conscious of their later incentive to cheat on it we also uncover puzzles for established theory and identify elements that a richer theory should encompass especially regarding the role of communication in collusion our window into the inner workings of a cartel is a remarkable series of notes on the weekly meetings of the sugar institute this trade association was formed in december 1927 in the wake of several years of falling margins and excess capacity by 14 firms comprising nearly all the cane sugar refining capacity in the united states it operated until 1936 when the supreme court ruled its practices illegal among the top executives in regular attendance at the meetings was louis v place vice president of mccahan a midsize refinery in philadelphia place who was in charge of all activities of the company except production and raw sugar purchases wrote over 500 pages of single spaced detailed

investments holdup and the form of market contracts the authors analyze incomplete contracts to induce efficient investment with exogenous switching costs fixed price contracts are efficient generate some rigidity in prices are renegotiated intermittently by possibly small amounts and when inflation is positive generate asymmetric responses to shocks all consistent with evidence on prices and wages with two sided specific investments efficiency requires prices to have sufficient escalator clauses to avoid renegotiation as observed in many long term contracts a third case with one sided specific investments can generate take or pay contracts and explain why firms sometimes pay for specific investments that appear to benefit employees directly

cartel stability and product differentiation abstract this paper employs a supergame theoretic model of collusion to analyze the effects of different levels of product differentiation on cartel stability in contrast to earlier work the ability of the parties to reach an agreement is assumed here the focus is on how greater product homogeneity increases both the gain to cheating on a collusive agreement and the magnitude of the punishments that follow a defection the total effect on the likelihood a cartel is stable is therefore unclear two particular differentiated products models are then used to demonstrate that contrary to the conventional view greater homogeneity can reduce cartel stability

collusion in differentiated duopolies revisited abstract in a letter previously published in this journal rothschild 1992 rothschild r 1992 on the sustainability of collusion in differentiated duopolies economics letters 40 33 37 claims to obtain results in contrast with those obtained by deneckere 1983 deneckere r 1983 duopoly supergames with product differentiation economics letters 11 37 42 we show however that taking correctly into account non negativity constraints on output rothschild s formulation yields the same conclusions as deneckere s

strategic pricing models and interpretation of price war data abstract price wars cartel breakdowns and other seemingly disequilibrium pricing phenomena are examined questions of interest include when do breakdowns occur how long do they last what determines their severity and are they characterized by increased cross sectional price dispersion and or temporal price volatility the first half of the paper explains how the choice of punishment strategy the specification of the stochastic shocks to the system and the assumptions regarding observability determine the pricing dynamics implicit in several theoretical price war models theories are classified into imperfect monitoring models in which players actions cannot be observed learning models in which structural parameters are unknown to the players and cyclical models in which observability is perfect but business cycles affect the difficulty of colluding the second half in contrast examines data on prices actually set by firms in industries which are subject to periodic wars when the models are confronted with the data we can see how well oligopoly theory explains the behavior of the firms in these industries the object of the exercise is not to pick a winner instead the role of industry characteristics in determining pricing dynamics is assessed and the reasons why simple models may fail to explain complex pricing patterns are examined finally directions for future research are suggested by the empirical regularities which are uncovered

oligopoly supergames some empirical evidence on prices and margins this paper is a panel data study on the behavior of prices and margins of oligopolies involved in repeated games the authors examine two supergame models which generate very different predictions about the cyclical behavior of prices and margins evidence on the levels of price cost margins indicates that oligopolies achieve equilibria that more closely resemble a one shot cournot nash outcome than monopoly the authors find however that industries with high price cost margins exhibit cyclical price behavior which is quite different from that of unconcentrated industries little evidence of price wars during either recessions or booms is found copyright 1987 by blackwell publishing ltd

a theory of conscious parallelism abstract in this paper the rationality of conscious parallelism is studied within the context of a dynamic oligopoly model the doctrine of conscious parallelism is modelled as the outcome of a signalling game in which the rules of response are specified axiomatically this will result in a unique solution to the oligopoly problem that is based on firms need to have consistent expectations that subsequently generate collusive behaviour this model can then be used to more precisely define the conditions that facilitate or limit oligopolistic coordination as found in the traditional industrial organization literature

subgame perfect reaction function equilibria in discounted duopoly supergames are trivial abstract this paper is concerned with infinitely repeated duopoly games with discounting a question which has been open since friedman s rev econ stud 35 1968 257 272 reaction function article is settled for a general class of games the question is wheter nontrivial reaction function equilibria can be subgame perfect this question is answered in the negative such equilibria must be trivial in the sense of prescribing the stage game noncooperative equilibrium actions in every period independent of prior history

the effects of statutory minimum rates of pay on employment in great britain estimates of the employment effects of statutory minimum rates of pay are derived for great britain using a constant elasticity of substitution production function the author estimates the partial elasticities of substitution in those industries covered by statutory minimum rates to be between 0 45 and 0 85 he then develops a bargaining model and estimates that the elasticity of the average wage rate in these industries with respect to the statutory minimum rate is zero for men and between 0 07 and 0 15 for women combining these estimates yields 0 06 as the approximate total employment elasticity of statutory minimum rates copyright 1989 by royal economic society

a theory of dynamic oligopoly ii price competition kinked demand curves and edgeworth cycles we provide game theoretic foundations for the classic kinked demand curve equilibrium and edgeworth cycle we analyze a model in which firms take turns choosing prices the model is intended to capture the idea of reactions based on short run commitment in a markov perfect equilibrium mpe a firm s move in any period depends only on the other firm s current price there are multiple mpe s consisting of both kinked demand curve equilibria and edgeworth cycles in any mpe profit is bounded away from the bertrand equilibrium level we show that a kinked demand curve at the monopoly price is the unique symmetric renegotiation proof equilibrium when there is little discounting we then endogenize the timing by allowing firms to move at any time subject to short run commitments we find that firms end up alternating thus vindicating the ad hoc timing assumption of our simpler model we also discuss how the model can be enriched to provide explanations for excess capacity and market sharing keiiwords tacit collusion markov perfect equilibrium kinked demand curve edgeworth cycle excess capacity market sharing endogenous timing

non trivial subgame perfect duopoly equilibria can be supported by continuous reaction functions abstract this paper demonstrates that non trivial subgame perfect duopoly equilibria can be supported by continuous reaction functions when previous period actions of both firms are arguments of reaction functions continuity imposes essentially no restrictions on the set of equilibria

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

instrument instability and short term monetary control abstract the literature on instrument instability tends support to a policy of smoothing interest rates it contends that rigid adherence to a monetary rule would bring about explosive interest rate movements this contention is examined using a simple model which incorporates rational expectations the results suggest that instrument instability is associated with interest rate smoothing rather than with short term control of the money supply furthermore policy that attempts to stabilize interest rates may itself account for empirical findings which have hitherto been viewed as evidence that instrument instability would occur if the money supply were closely controlled

the kinked demand curve a game theoretic approach in a simple model of duopoly firms price moves are modelled as an extensive form game where firms can respond to undercutting without delay when firms are not too dissimilar kinked demand strategies enforcing an arbitrary price may be nash equilibria however these strategies are dominated and perfect equilibrium is unique at the minimum optimal common price rather than implying price rigidity kinked demand strategies are a device for ensuring compliance with a collusive price leadership

vancouver s gasoline price wars an empirical exercise in uncovering supergame strategies this paper uses a unique data set to determine which dynamic model of tacit collusion best describes behaviour in a particular industry the area investigated is a region of the vancouver british columbia retail gasoline market players are service station managers who compete daily firms choose price in each period using strategies that depend on prices chosen in the previous period periodically unanticipated demand shocks precipitate price wars when shocks occur the firms in the market must determine the new demand conditions and adjust their strategies from an econometric point of view slopes of intertemporal reaction functions are latent variables the resulting system of equations with time varying parameters is estimated via the kalman filter different repeated game oligopoly models correspond to different transition matrices for the latent variables the models can thus be assessed in terms of their power to explain firm behaviour in this market

subgame perfect equilibrium with continuous reaction functions abstract earlier efforts by friedman examined infinite horizon oligopolies trying and failing to show existence of subgame perfect nash equilibria with the firms strategies being continuous reaction functions here in a typical game theoretic model with discounting we prove the existence of such equilibria the equilibrium strategies mimic trigger strategies in their method of operation but are continuous so that small defections from equilibrium actions result in small per period punishments we prove our results by constructing equilibria in a fashion analogous to that found in proofs of folk theorems in repeated games

conjectural variations strategies in accelerated cournot games abstract a family of constant conjectural variations strategies is defined and examined in the natural context of infinitely repeated cournot duopoly games with discounting it is shown that any pair of linear reaction functions in the family gives rise to a unique pair of quantities in stationary equilibrium as the conjectures and discount parameter vary the sum of the stationary quantities will vary anywhere between the competitive and the monopoly outcomes equilibrium is strongly stable and credible in the sense of exhibiting a variation of selten s subgame perfection provided that firms can react quickly enough to one another s actions

tacit collusion with price matching punishments abstract tacit collusion is explored under a strategy in which loosely speaking firms match the lowest price set by any firm in the previous period conditions are provided under which this strategy supports collusive outcomes in a subgame perfect equilibrium in contrast to traditional results the highest collusive price is always lower than the monopoly price it corresponds to the unique nash equilibrium price when upward and downward price deviations are matched our paper provides a game theoretic interpretation of the old kinked demand curve theory which unlike earlier attempts does not depart from standard timing assumptions to do so

price wars and the stability of collusion a study of the pre world war i bromine industry between 1885 and 1914 us bromine producers colluded to raise prices and pro ts this collusion was disrupted by price wars bromine price wars are compared with the green porter and abreu pearce stacchetti models some price wars resulted from the imperfect monitoring problems which motivate these models several empirical implications of the aps model are borne out but the bromine industry s price wars were generally milder than contemplated by aps more severe price wars were part of a bargaining process in which rms tried to force renegotiation to a new collusive equilibrium with a diierent distribution of rents

tacit collusion with imperfect monitoring in the canadian manufacturing industry an empirical study this article undertakes a cross sectoral analysis of a salient empirical implication of the model of tacit collusion advanced by abreu pearce and stachetti 1986 specifically we assess the prevalence of a first order markovian process for alternating between price wars and collusive periods through nonparametric tests the analysis focuses on 30 different industries in canada the evidence provides weak support for optimal collusion in one industry which is consistent with the idea that such kind of collusive arrangements is unusual or if collusion is all too common that price wars as deviations from collusion are rare

collusive price rigidity under price matching punishments by analysing an infinitely repeated game where unit costs alternate stochastically between low and high states and where firms follow a price matching punishment strategy we demonstrate that the best collusive prices are rigid over time when the two cost levels are sufficiently close this provides game theoretic support for the results of the kinked demand curve in contrast to the kinked demand curve it also generates predictions regarding the level and the determinants of the best collusive price which in turn has implications for the corresponding collusive profits the relationships between such price rigidity and the expected duration of a high cost phase the degree of product differentiation and the number of firms in the market are also investigated

do low price guarantees guarantee low prices evidence from competition between amazon and big box stores it has long been understood in theory that price match guarantees can be anticompetitive but to date scant empirical evidence is available outside of some narrow markets this paper broadens the scope of empirical analysis studying a wide range of products sold on a national online market using an algorithm that extracts data from charts i obtain a novel source of data from online price trackers i examine prices of goods sold on amazon before and after two big box stores target and best buy announced a guarantee to match amazon s prices employing both difference in difference and regression discontinuity approaches i robustly estimate a positive causal effect of six percentage points the effect was heterogeneous with larger price increases for initially lower priced items my results support anticompetitive theories which predict price increases for amazon a firm that did not adopt the guarantee and are consistent with plausible mechanisms for the heterogeneous impact

the effects of product differentiation on collusive pricing abstract using the spatial competition framework of hotelling 1929 this paper explores the relationship between the degree of product differentiation and the ability of firms to collude with respect to price we show that the minimum discount factor required to support the joint profit maximum as an equilibrium outcome monotonically increases as products become better substitutes when the joint profit maximum cannot be supported the optimal collusive price is shown to decline as products become more substitutable these findings suggest that firms producing stronger substitutes tend to find it tougher to collude in terms of their product price

wage differentials employer size and unemployment the unique equilibrium solution to a game in which a continuum of individual employers choose permanent wage offers and a continuum of workers search by sequentially sampling from the set of offers is characterized wage dispersion is a robust outcome provided that workers search while employed as well as when unemployed the unique nondegenerate equilibrium distribution of wage offers is constructed for three cases 1 identical workers and employers 2 identical employers and an atomless distribution of worker supply prices and 3 identical workers and an atomless distribution of job productivities copyright 1998 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

the effects of minimum wages on employment theory and evidence from britain recent work on the economic effects of minimum wages has stressed that the standard economic model where increases in minimum wages depress employment is not supported by empirical work in some labor markets we present a general theoretical model whereby employers have some degree of monopsony power which allows minimum wages to have the conventional negative impact on employment but which also allows for a neutral or positive impact studying the industry based british wages councils between 1975 and 1992 we find that minimum wages significantly compress the distribution of earnings but do not have a negative impact on employment

comment on david neumark and william wascher employment effects of minimum and subminimum wages panel data on state minimum wage laws in their article published in the minimum wage research symposium in the october 1992 issue of this journal industrial and laborrelations review volume 45 number 1 pp 55 81 david neumark and william wascher claim to find empirical support for three propositions 1 a higher minimum wage leads to a lower teenage employmentpopulation rate 2 the effect of the minimum wage on employment can be seen within a year but becomes stronger after two years and 3 in states with legal subminimum wages a significant fraction of teenage employees are paid a subminimum wage and the availability of a subminimum wage blunts the disemployment effect of the minimum wage the same symposium contains three papers by us that present empirical evidence suggesting conclusions opposite those of neumark and wascher 1 since neumark and