Conflicts with Multiple Battlefields

This paper examines conflicts in which performance is measured by the players' success or failure in multiple component conflicts, commonly termed "battlefields." In multi-battlefield conflicts, behavioral linkages across battlefields depend both on the technologies of conflict within each battlefield and the nature of economies or diseconomies in how battlefield out- comes and costs aggregate in determining payoffs in the overall conflict.Con ict, Contest, Battleeld, Colonel Blotto Game, Auction, Lottery

Multi-battle contests

We study equilibrium in a multistage race in which players compete in a sequence of simultaneous move component contests. Players may win a prize for winning each component contest, as well as a prize for winning the overall race. Each component contest is an all-pay auction with complete information. We characterize the unique equilibrium analytically and demonstrate that it exhibits endogenous uncertainty. Even a large lead by one player does not fully discourage the other player, and each feasible state is reached with positive probability in equilibrium (pervasiveness). Total effort may exceed the value of the prize by a factor that is proportional to the maximum number of stages. Important applications are to war, sports, and R&D contests and the results have empirical counterparts there

Inefficient Redistribution and Inefficient Redistributive Politics

This paper examines the effect of inefficient redistribution in Myerson’s (1993) model of redistributive politics. Regardless of the absolute levels of the efficiency of political parties’ transfers to different voter segments, parties have incentive to (stochastically) shift resources away from voter segments with large relative efficiency gaps between the two parties’ transfers towards voter segments with smaller relative efficiency gaps. Because of this dependence on relative, and not absolute, levels of efficiency, the parties’ optimal strategies may lead to large discrepancies between the sum of the budgetary transfers and the sum of the effective transfers. At the extreme, in the spirit of Magee, Brock, and Young (1989), we obtain “black hole” inefficiency. When the model is extended to allow for loyal voter segments and loyalty to a party is positively related to the efficiency of that party’s transfers to the segment, the incentives leading to black hole inefficiency become even stronger.

Tacit Collusion and Capacity Withholding in Repeated Uniform Price Auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this outcome. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor above which the perfectly collusive outcome with equal sharing is sustainable on a stationary path. Under the Market Clearing Price rule, only one step is required. That is, within the class of step bidding functions with a finite number of steps, maximal collusion is attained with simple price-quantity strategies exhibiting capacity withholding.Auction; Capacity; Collusion; Electricity Market; Supply Function

Is the 50-State Strategy Optimal?

In 2005, the Democratic National Committee adopted the 50-state strategy in lieu of the strategy of focusing solely on battleground states. The rationale given for this move is that campaign expenditures are durable outlays that impact both current and future campaigns. This paper investigates the optimality of the 50-state strategy in a simple dynamic game of campaign resource allocation in which expenditures act as a form of investment. Neither the 50-state nor the battleground-states strategy is likely to arise in equilibrium. Instead, parties employ a modified battleground-states strategy in which they stochastically target non-battleground states.Political Campaigns, Dynamic Contests, Elections, All-Pay Auction,War of Attrition

Inefficient redistribution and inefficient redistributive politics

This paper examines the effect of inefficient redistribution in Myerson’s (1993) model of redistributive politics. Regardless of the absolute levels of the efficiency of political parties’ transfers to different voter segments, parties have incentive to (stochastically) shift resources away from voter segments with large relative efficiency gaps between the two parties’ transfers towards voter segments with smaller relative efficiency gaps. Because of this dependence on relative, and not absolute, levels of efficiency, the parties’ optimal strategies may lead to large discrepancies between the sum of the budgetary transfers and the sum of the effective transfers. At the extreme, in the spirit of Magee, Brock, and Young (1989), we obtain „black hole” inefficiency. When the model is extended to allow for loyal voter segments and loyalty to a party is positively related to the efficiency of that party’s transfers to the segment, the incentives leading to black hole inefficiency become even stronger. -- Diese Arbeit untersucht die Auswirkung von ineffizienter Umverteilungspolitk im Rahmen des Modells von Myerson (1993). Parteien versuchen, Wählersegmente für sich zu gewinnen, indem sie ihnen Transferzahlungen zusagen. Einzelne Wählersegmente unterscheiden sich in der Effizienz, mit der sich die Transferzahlungen einer bestimmten Partei in einen resultierenden Nutzengewinn für den Wähler übersetzen. Für die Parteien entsteht ein Anreiz, (stochastisch) Ressourcen hin zu Wählersegmenten zu verlagern, bei denen die Transfers von zwei verschiedenen Parteien einen relativ kleinen Unterschied in ihrem Effizienzniveau aufweisen, ungeachtet des absoluten Effizienzniveaus der Transferzahlung. Aufgrund dieser Abhängigkeit von relativen und nicht absoluten Effizienzniveaus können die Gleichgewichtsstrategien der Parteien zu großen Unterschieden zwischen der Summe der getätigten Transfers und der Summe der effektiv erhaltenen Transfers führen. Im Extremfall erhalten wir „black hole“-Ineffizienz wie in Magee, Brock und Young (1989). Eine Erweiterung des Modells um loyale Wählersegmente, bei der Loyalität zu einer Partei in positivem Bezug zur Effizienz der von dieser Partei erhaltenen Transfers steht, verstärkt die Anreize, die zu „black hole“-Ineffizienz führen.Redistributive politics,redistribution,inefficiency

Tacit Collusion and Capacity Withholding in Repeated Uniform Price Auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this out-come. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factorAuction, Capacity, Collusion, Electricity Market, Supply Function

Endogenous Rationing, Price Dispersion, and Collusion in Capacity Constrained Supergames.

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival’s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with successful collusion, it may be a requirement of successful collusion.Bertrand-Edgeworth ; Supergame ; Collusion ; Capacity

Coalitional Colonel Blotto games with application to the economics of alliances

This paper examines a multi-player and multi-front Colonel Blotto game in which one player, A, simultaneously competes in two disjoint Colonel Blotto games, against two separate opponents, 1 and 2. Prior to competing in the games, players 1 and 2 have the opportunity to form an alliance to share their endowments of a one-dimensional resource (e.g., troops, military hardware, money). This paper examines „non-cooperative“ alliances in which only individually rational ex ante transfers of the resource are allowed. Once these transfers take place, each alliance member maximizes his payoff in his respective Colonel Blotto game, given his resource constraint and player A's allocation of its endowment across the two games. No ex post transfers are enforceable. Remarkably, there are several ranges of parameters in which endogenous unilateral transfers take place within the alliance. That is, one player gives away resources to his ally, who happily accepts the gift. Unilateral transfers arise because they lead to a strategic shift in the common opponent's force allocation away from the set of battlefields of the player making the transfer, towards the set of battlefields of the player receiving the transfer. Our result demonstrates that there exist unilateral transfers for which the combination of direct and strategic effects benefits both allies. This stands in stark contrast to the previous literature on alliances (see Sandler and Hartley, 2001), which relies on the assumption of pure or impure public goods. -- Diese Arbeit analysiert Colonel Blotto-Spiele mit mehr als zwei Spielern, die an mindestens zwei Fronten miteinander kämpfen. Spieler A kämpft gleichzeitig in zwei Colonel Blotto-Spielen mit zwei verschiedenen Kontrahenten, B1 und B2. Die Kontrahenten können vor der eigentlichen Konfliktphase eine Allianz eingehen. Das erlaubt es ihnen ihre Mengen an einer homogenen Konfliktressource (Truppen, Waffen, Geld) untereinander zu transferieren. Das Papier untersucht dabei „nicht-kooperative“ Allianzen. Darunter wird verstanden, dass der Einsatz der transferierten Ressourcen auf den jeweiligen Konfliktschauplätzen von dem jeweiligen Spieler B1 bzw. B2 in seinem eigenen Interesse eingesetzt wird und Seitenzahlungen im Anschluss an die Konfliktphase ausgeschlossen sind. Es zeigt sich, dass es dennoch zu einseitigen und freiwilligen Ressourcentransfers der Spieler B1 und B2 im Vorfeld des Konflikts kommen kann, dass also beispielsweise B1 an B2 z.B. Waffen liefert, B2 diese als Geschenk akzeptiert und sich beide, B1 und B2 besser stellen. Ursache für die Besserstellung ist der strategische Effekt solcher Transfers auf das Kampfverhalten von A, der seine Kampfkraft vom Kampfgeschehen mit B1 zum Kampfgeschehen mit B2 verlagert. Das Ergebnis widerspricht den früheren Ergebnissen zu Allianzen (vgl. Sandler und Hartley, 2001), das im Kontext der privaten Bereitstellung öffentlicher Güter erzielt wurde.Alliance,noncooperative game,Colonel Blotto game,self-enforcing,exploitation,commitment

The lifeboat problem

We study an all-pay contest with multiple identical prizes ("lifeboat seats"). Prizes are partitioned into subsets of prizes ("lifeboats"). Players play a twostage game. First, each player chooses an element of the partition ("a lifeboat"). Then each player competes for a prize in the subset chosen ("a seat"). We characterize and compare the subgame perfect equilibria in which all players employ pure strategies or all players play identical mixed strategies in the first stage. We find that the partitioning of prizes allows for coordination failure among players when they play nondegenerate mixed strategies and this can shelter rents and reduce rent dissipation compared to some of the less efficient pure strategy equilibria