Dynamic price competition with fixed capacities

Many revenue management (RM) industries are characterized by (a) fixed capacities in theshort term (e.g., hotel rooms, seats on an airline flight), (b) homogeneous products (e.g., twoairline flights between the same cities at similar times), and (c) customer purchasing decisionslargely influenced by price. Competition in these industries is also very high even with just twoor three direct competitors in a market. However, RM competition is not well understood andpractically all known implementations of RM software and most published models of RM donot explicitly model competition. For this reason, there has been considerable recent interestand research activity to understand RM competition. In this paper we study price competitionfor an oligopoly in a dynamic setting, where each of the sellers has a fixed number of unitsavailable for sale over a fixed number of periods. Demand is stochastic, and depending on howit evolves, sellers may change their prices at any time. This reflects the fact that firms constantly,and almost costlessly, change their prices (alternately, allocations at a price in quantity-basedRM), reacting either to updates in their estimates of market demand, competitor prices, orinventory levels. We first prove existence of a unique subgame-perfect equilibrium for a duopoly.In equilibrium, in each state sellers engage in Bertrand competition, so that the seller withthe lowest reservation value ends up selling a unit at a price that is equal to the equilibriumreservation value of the competitor. This structure hence extends the marginal-value conceptof bid-price control, used in many RM implementations, to a competitive model. In addition,we show that the seller with the lowest capacity sells all its units first. Furthermore, we extendthe results transparently to n firms and perform a number of numerical comparative staticsexploiting the uniqueness of the subgame-perfect equilibrium.

Disability, capacity for work and the business cycle: An international perspective

An important policy issue in recent years concerns the number of people claimingdisability benefits for reasons of incapacity for work. We distinguish between workdisability , which may have its roots in economic and social circumstances, and healthdisability which arises from clear diagnosed medical conditions. Although there is a linkbetween work and health disability, economic conditions, and in particular the businesscycle and variations in the risk of unemployment over time and across localities, mayplay an important part in explaining both the stock of disability benefit claimants andinflows to and outflow from that stock. We employ a variety of cross?country andcountry?specific household panel data sets, as well as administrative data, to testwhether disability benefit claims rise when unemployment is higher, and also toinvestigate the impact of unemployment rates on flows on and off the benefit rolls. Wefind strong evidence that local variations in unemployment have an importantexplanatory role for disability benefit receipt, with higher total enrolments, loweroutflows from rolls and, often, higher inflows into disability rolls in regions and periodsof above?average unemployment. Although general subjective measures of selfreporteddisability and longstanding illness are also positively associated withunemployment rates, inclusion of self?reported health measures does not eliminate thestatistical relationship between unemployment rates and disability benefit receipt;indeed including general measures of health often strengthens that underlyingrelationship. Intriguingly, we also find some evidence from the United Kingdom and theUnited States that the prevalence of self?reported objective specific indicators ofdisability are often pro?cyclical that is, the incidence of specific forms of disability arepro?cyclical whereas claims for disability benefits given specific health conditions arecounter?cyclical. Overall, the analysis suggests that, for a range of countries and datasets, levels of claims for disability benefits are not simply related to changes in theincidence of health disability in the population and are strongly influenced by prevailingeconomic conditions. We discuss the policy implications of these various findings.

Psychological pressure in competitive environments: Evidence from a randomized natural experiment

Much like cognitive abilities, emotional skills can have major effects on performance and economic outcomes. This paper studies the behavior of professionalsubjects involved in a dynamic competition in their own natural environment. Thesetting is a penalty shoot-out in soccer where two teams compete in a tournamentframework taking turns in a sequence of five penalty kicks each. As the kicking order is determined by the random outcome of a coin flip, the treatment and control groups are determined via explicit randomization. Therefore, absent any psychological effects, both teams should have the same probability of winning regardless of the kicking order. Yet, we find a systematic first-kicker advantage. Using data on 2,731 penalty kicks from 262 shoot-outs for a three decade period, we find that teams kicking first win the penalty shoot-out 60.5% of the time. A dynamic panel data analysis shows that the psychological mechanism underlying this result arises from the asymmetry in the partial score. As most kicks are scored, kicking first typically means having the opportunity to lead in the partial score, whereas kicking second typically means lagging in the score and having the opportunity to, at most, get even. Having a worse prospect than the opponent hinders subjects' performance.Further, we also find that professionals are self-aware of their own psychological effects. When a recent change in regulations gives winners of the coin toss the chance to choose the kicking order, they rationally react to it by systematically choosing to kick first. A survey of professional players reveals that when asked to explain why they prefer to kick first, they precisely identify the psychological mechanism for which we find empirical support in the data: they want to lead in the score inorder to put pressure on the opponent.

Proving the performance of a new revenue management system

Revenue management (RM) is a complicated business process that can best be described ascontrol of sales (using prices, restrictions, or capacity), usually using software as a tool to aiddecisions. RM software can play a mere informative role, supplying analysts with formatted andsummarized data who use it to make control decisions (setting a price or allocating capacity fora price point), or, play a deeper role, automating the decisions process completely, at the otherextreme. The RM models and algorithms in the academic literature by and large concentrateon the latter, completely automated, level of functionality.A firm considering using a new RM model or RM system needs to evaluate its performance.Academic papers justify the performance of their models using simulations, where customerbooking requests are simulated according to some process and model, and the revenue perfor-mance of the algorithm compared to an alternate set of algorithms. Such simulations, whilean accepted part of the academic literature, and indeed providing research insight, often lackcredibility with management. Even methodologically, they are usually awed, as the simula-tions only test \within-model" performance, and say nothing as to the appropriateness of themodel in the first place. Even simulations that test against alternate models or competition arelimited by their inherent necessity on fixing some model as the universe for their testing. Theseproblems are exacerbated with RM models that attempt to model customer purchase behav-ior or competition, as the right models for competitive actions or customer purchases remainsomewhat of a mystery, or at least with no consensus on their validity.How then to validate a model? Putting it another way, we want to show that a particularmodel or algorithm is the cause of a certain improvement to the RM process compared to theexisting process. We take care to emphasize that we want to prove the said model as the causeof performance, and to compare against a (incumbent) process rather than against an alternatemodel.In this paper we describe a \live" testing experiment that we conducted at Iberia Airlineson a set of flights. A set of competing algorithms control a set of flights during adjacentweeks, and their behavior and results are observed over a relatively long period of time (9months). In parallel, a group of control flights were managed using the traditional mix of manualand algorithmic control (incumbent system). Such \sandbox" testing, while common at manylarge internet search and e-commerce companies is relatively rare in the revenue managementarea. Sandbox testing has an undisputable model of customer behavior but the experimentaldesign and analysis of results is less clear. In this paper we describe the philosophy behind theexperiment, the organizational challenges, the design and setup of the experiment, and outlinethe analysis of the results. This paper is a complement to a (more technical) related paper thatdescribes the econometrics and statistical analysis of the results.

On Rothschild-Stiglitz as competitive pooling

Dubey and Geanakoplos [2002] have developed a theory of competitive pooling, which incorporates adverse selection and signaling into general equilibrium. By recasting the Rothschild-Stiglitz model of insurance in this framework, they find that a separating equilibrium always exists and is unique.We prove that their uniqueness result is not a consequence of the framework, but rather of their definition of refined equilibria. When other types of perturbations are used, the model allows for many pooling allocations to be supported as such: in particular, this is the case for pooling allocations that Pareto dominate the separating equilibrium.

Consumer choice in competitive location models: Formulations and heuristics

A new direction of research in Competitive Location theory incorporatestheories of Consumer Choice Behavior in its models. Following thisdirection, this paper studies the importance of consumer behavior withrespect to distance or transportation costs in the optimality oflocations obtained by traditional Competitive Location models. To dothis, it considers different ways of defining a key parameter in thebasic Maximum Capture model (MAXCAP). This parameter will reflectvarious ways of taking into account distance based on several ConsumerChoice Behavior theories. The optimal locations and the deviation indemand captured when the optimal locations of the other models are usedinstead of the true ones, are computed for each model. A metaheuristicbased on GRASP and Tabu search procedure is presented to solve all themodels. Computational experience and an application to 55-node networkare also presented.

Tracking the invisible hand: Convergence of double auctions to competitive equilibrium

Economics is the science of want and scarcity. We show that want andscarcity, operating within a simple exchange institution (double auction),are sufficient for an economy consisting of multiple inter--related marketsto attain competitive equilibrium (CE). We generalize Gode and Sunder's(1993a, 1993b) single--market finding to multi--market economies, andexplore the role of the scarcity constraint in convergence of economies to CE.When the scarcity constraint is relaxed by allowing arbitrageurs in multiple markets to enter speculative trades, prices still converge to CE,but allocative efficiency of the economy drops. \\Optimization by individual agents, often used to derive competitive equilibria,are unnecessary for an actual economy to approximately attain such equilibria.From the failure of humans to optimize in complex tasks, one need not concludethat the equilibria derived from the competitive model are descriptivelyirrelevant. We show that even in complex economic systems, such equilibriacan be attained under a range of surprisingly weak assumptions about agentbehavior.

Supply chain management as a competitive advantage in the Spanish grocery sector

Adversarial relationships have long dominated business relationships,but Supply Chain Management (SCM) entails a new perspective. SCM requiresa movement away from arms-length relationships toward partnership stylerelations. SCM involves integration, co-ordination and collaborationacross organisations and throughout the supply chain. It means that SCMrequires internal (intraorganisational) and external (interorganisational)integration. This paper analyses the relationship between internal andexternal integration processes, their effect on firms performance andtheir contribution to the achievement of a competitive advantage.Performance improvements are analysed through costs, stock out and leadtime reductions. And, the achievement of a better competitive positionis measured by comparing the firm s performance with its competitors performance. To analyse this, an empirical study has been conducted inthe Spanish grocery sector.

A note on the convergence to competitive equilibria in economies with moral hazard

We examine the conditions under which competitive equilibria can beobtained as the limit, when the number of strategic traders getslarge, of Nash equilibria in economies with asymmetric informationon agents' effort and possibly imperfect observability of agents'trades. Convergence always occur when either effort is publiclyobserved (no matter what is the information available tointermediaries on agents' trades); or effort is private informationbut agents' trades are perfectly observed; or no information at allis available on agents' trades. On the other hand, when eachintermediary can observe its trades with an agent, but not theagent's trades with other intermediaries, the (Nash) equilibriawith strategic intermediaries do not converge to any of thecompetitive equilibria, for an open set of economies. The source ofthe difficulties for convergence is the combination of asymmetricinformation and the restrictions on the observability of tradeswhich prevent the formation of exclusive contractual relationshipsand generate barriers to entry in the markets for contracts.

Incorporating waiting time in competitive location models: Formulations and heuristics

In this paper we propose a metaheuristic to solve a new version of the Maximum CaptureProblem. In the original MCP, market capture is obtained by lower traveling distances or lowertraveling time, in this new version not only the traveling time but also the waiting time willaffect the market share. This problem is hard to solve using standard optimization techniques.Metaheuristics are shown to offer accurate results within acceptable computing times.

Forward induction and the excess capacity puzzle: An experimental investigation

While the theoretical industrial organization literature has long arguedthat excess capacity can be used to deter entry into markets, there islittle empirical evidence that incumbent firms effectively behave in thisway. Bagwell and Ramey (1996) propose a game with a specific sequence ofmoves and partially-recoverable capacity costs in which forward inductionprovides a theoretical rationalization for firm behavior in the field. Weconduct an experiment with a game inspired by their work. In our data theincumbent tends to keep the market, in contrast to what the forwardinduction argument of Bagwell and Ramey would suggest. The results indicatethat players perceive that the first mover has an advantage without havingto pre-commit capacity. In our game, evolution and learning do not driveout this perception. We back these claims with data analysis, atheoretical framework for dynamics, and simulation results.

Organized vs. competitive corruption

We study bureaucratic corruption in a model in which a constituencysets required levels for a given set of activities. Each activity iscarried out by an external provider, and its realization is supervisedby a bureaucrat. While bureaucrats are supposed to act on behalf of theconstituency, they can decide to be corrupt and allow providers todeliver lower activity levels than contracted in exchange for a bribe.Given this, the constituency sets the optimal activity levels weighingoff the value of activity levels, their costs, as well as the possibilityfor the bureaucrats to be corrupt. We use this setup to study the impacton equilibrium corruption of the degree of decentralization of corruption.To do this we compute equilibrium corruption in two different settings:1) Each bureaucrat acts in such a way as to maximize his own individualutility (competitive corruption); 2) An illegal syndicate oversee thecorruption decisions of the population of bureaucrats in such a way asto maximize total proceeds from corruption (organized corruption). Weshow that, since average corruption payoff is increasing in the activitylevels set by the constituency, and since the latter responds to highlevels of corruption by reducing required activity levels, in equilibriumthe illegal syndicate acts in such a way as to restrain the total numberof corrupt transactions, so that corruption is lower when it is organizedthan when it is competitive.

A non-quasi-competitive Cournot oligopoly with stability

This paper presents a classical Cournot oligopoly model with some peculiar features: it is non--quasi--competitive as price under N-poly is greater than monopoly price; Cournot equilibrium exists and is unique with each new entry; the successive equilibria after new entries are stable under the adjustment mechanism that assumes that actual output of each seller is adjusted proportionally to the difference between actual output and profit maximizing output. Moreover, the model tends to perfect competition as N goes to infinity, reaching the monopoly price again.

Surviving in a competitive spatial market: The threshold capture model

Most facility location decision models ignore the fact that for a facility to survive it needs a minimum demand level to cover costs. In this paper we present a decision model for a firm thatwishes to enter a spatial market where there are several competitors already located. This market is such that for each outlet there is a demand threshold level that has to be achievedin order to survive. The firm wishes to know where to locate itsoutlets so as to maximize its market share taking into account the threshold level. It may happen that due to this new entrance, some competitors will not be able to meet the threshold and therefore will disappear. A formulation is presented together with a heuristic solution method and computational experience.

Buffer Capacity Allocation: A method to QoS support on MPLS networks

This paper describes an optimized model to support QoS by mean of Congestion minimization on LSPs (Label Switching Path). In order to perform this model, we start from a CFA (Capacity and Flow Allocation) model. As this model does not consider the buffer size to calculate the capacity cost, our model- named BCA (Buffer Capacity Allocation)- take into account this issue and it improve the CFA performance. To test our proposal, we perform several simulations; results show that BCA model minimizes LSP congestion and uniformly distributes flows on the network