We employ a hierarchical Stackelberg model with k≥ 2 firms to examine an oligopoly where firms supplying homogeneous products compete for market share under price leadership. Within this setting, both market clearing and oversupply are potential market states, and which one arises as the equilibrium is determined endogenously. Regarding the analysis, since the standard best-response approach is inapplicable to this setting, we adopt the inverted best-response method of Kahana and Klunover (2018) and Hinnosaar (2024). In relatively small markets, market clearing occurs with an early-mover advantage and converges to efficiency as competition intensifies. In larger markets, oversupply emerges, with an early-mover advantage persisting except in the duopoly case, where leader and follower earn equal profits. Furthermore, under oversupply, the price is rigid to competition intensity and marginal cost, so greater competition or lower costs only increase the likelihood of oversupply. These results suggest that oversupply may persist as a structural feature in highly competitive oligopolies due to endogenously determined price rigidity.
I examine a seller’s choice between simple rules of bargaining and price determination when the seller’s cost is private, the buyer’s value is private, and with positive probability the buyer privately knows a rival price. One examined rule is price matching (or ‘best price guarantee’). Introducing the bargaining setup to its analysis reveals its multiple salient and attractive features in one simple framework. The seller able to choose this raises its posted or listed price to its monopoly level; sells to more buyer types (realized values), price discriminating between them; and allows for effective matching of rival prices below its posted price. And although a low cost seller might be more likely to prefer price matching to a posted price with take it or leave it offer, its framing and execution prevents the buyer from exploiting any signal of the seller’s low cost from the choice of this rule. Moreover, ex ante buyer heterogeneity in information, ability, sophistication, or price elasticity is not necessary for a seller to use price matching to price discriminate between buyers.
In a stable matching problem, n agents on one side have individual preferences for n agents on another side as a potential match. A matching is called stable if no two unmatched agents prefer each other to their matches. Knuth demonstrated existence of preferences with exponentially many stable matchings, posing a question on expected number of stable matchings for a uniformly random problem instance. Using Knuth’s integral formula, the first author showed that this expectation is quite moderate, asymptotic to e^-1nlog n , n being the number of agents on each side. In this paper, relaxing stability notion, we declare matching stable if no unmatched pair of agents strongly prefer each other to their partners, with “strength” measured by a parameter ε >0 , ε =0 corresponding to classic stability. The expected number of ε -stable matchings is proved to be polynomially large if ε of order n^-1log n , but it explodes to become super-polynomially large once ε≫ n^-1log n .
This paper investigates two approaches to determining the leader of a coalition partition: the individual and the collective. In the first approach, each coalition in the partition chooses a representative, and then the leader is chosen from among all the representatives. In the second approach, the leading coalition is first chosen in the partition, and then the leader is chosen from among members of that coalition. Both approaches sometimes can be encountered in contests, sports competitions, or political elections. The paper delivers results on the existence of Nash-stable partitions depending on the approach and the probability of determining the leader. The existence of equilibrium in weakly dominant strategies is proved for the collective approach and the weight rule, and the necessary and sufficient conditions for a Nash-stable partition to exist were found for the ranking rule.
We consider a three-sided market where each buyer-seller pair can attain a profit only if there is a middleman that connects them. This profit does not depend on the identity of the middlemen, and each buyer and seller can take part in at most one partnership while middlemen can establish multiple partnerships, up to their capacity. We show that the core is non-empty and strictly contains the set of competitive equilibrium payoff vectors that coincides with the set of solutions of the dual q-assignment problem, where q is the total capacity of the middlemen.
