Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario

Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum nonlocality which sits between entanglement and Bell nonlocality. A set of correlations is Bell nonlocal if it does not admit a local hidden variable (LHV) model, while it is EPR nonlocal if it does not admit a local hidden variable-local hidden state (LHV-LHS) model. It is interesting to know what states can generate EPR-nonlocal correlations in the simplest nontrivial scenario, that is, two projective measurements for each party sharing a two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal full correlations (excluding marginal statistics) in this scenario if and only if it can generate Bell-nonlocal correlations. If full statistics (including marginal statistics) is taken into account, surprisingly, the same scenario can manifest the simplest one-way steering and the strongest hierarchy between steering and Bell nonlocality. To illustrate these intriguing phenomena in simple setups, several concrete examples are discussed in detail, which facilitates experimental demonstration. In the course of study, we introduce the concept of restricted LHS models and thereby derive a necessary and sufficient semidefinite-programming criterion to determine the steerability of any bipartite state under given measurements. Analytical criteria are further derived in several scenarios of strong theoretical and experimental interest.Comment: New results added, 13 pages, 3 figures; published in Phys. Rev.

On The Power to Hurt: Costly Conflict with Completely Informed States

Slantchev (2003, American Political Science Review, 97) studies a class of negotiation models to explain costly conflict between two completely informed nations. In one of his main propositions (Proposition 2.3), Slantchev provides a strategy profile to support the so-called extremal subgame perfect equilibrium, where one nation receives its lowest equilibrium payoff. By means of a counter example, we demonstrate the existence of an equilibrium with one nation's payoffs below the strategy profile provided in his Proposition 2.3 (Case 2).

Wage Bargaining under the National Labor Relations Act

Sections 8(a)(3) and 8(a)(5) of the National Labor Relations Act prevent a firm from unilaterally increasing the wage it pays the union during the negotiation of a new wage contract. To understand this regulation, we study a counterfactual negotiation model where the firm can temporarily increase compensation to its employees during wage negotiations. Comparing this to the case where the firm does not have this option, we show that the firm may strategically increase the union's temporary wage to upset the union's incentive to strike, decreasing the union's bargaining power, and shrinking the set of permanent wage contracts that may arise in a perfect equilibrium. As the union becomes more patient, the best possible equilibrium contract to the union gets worse. In the limit, the uniqueness and hence the full efficiency of the perfect equilibrium are restored. We also demonstrate that allowing the union to refuse the firm's temporary compensation does not affect the set of perfect equilibrium outcomesBargaining, Negotiation, Good Faith Bargaining

The Eeckhout Condition and the Subgame Perfect Implementation of Stable Matching

We investigate an extensive form sequential matching game of perfect information. We show that the subgame perfect equilibrium of the sequential matching game leads to the unique stable matching when the Eeckhout Condition (2000) for existence of a unique stable matching holds, regardless of the sequence of agents. This result does not extend to preferences that violate the Eeckhout Condition, even if there is a unique stable matching.Matching; unique stable matching; subgame perfect equilibrium

Multi-Agent Bilateral Bargaining with Endogenous Protocol

Consider a multilateral bargaining problem where negotiation is conducted by a sequence of bilateral bargaining sessions. We are interested in an environment where bargaining protocols are determined endogenously. During each bilateral bargaining session of Rubinstein (1982), two players negotiate to determine who leaves the bargaining and with how much. A player may either make an offer to his opponent who would then leave the game or demand to leave the game himself. Players' final distribution of the pie and a bargaining protocol constitute an equilibrium outcome. When discounting is not too high, we find multiple subgame perfect equilibrium outcomes, including inefficient ones. As the number of players increases, both the set of discount factors that support multiple equilibrium outcomes and the set of the first proposing player's equilibrium shares are enlarged. The inefficiency in equilibrium remains even as the discount factor goes to one.Multilateral bargaining

Antitrust enforcement with price-dependent fines and detection probabilities

We analyze the effectiveness of antitrust enforcement in repeated oligopoly models in which both fines and detection probabilities depend on the cartel price. Such fines reflect actual guidelines. Inspections based on monitoring of market prices imply endogenous detection probabilities. Without monitoring, fines that are either fixed or proportional to illegal gains cannot eradicate the monopoly price, but more-than-proportional fines can. Policy design with inspections based on price-monitoring implies that the profit-maximizing cartel price always lies below the monopoly price independently of the fine structure. These results offer partial support for the current practice of monitoring and more-than-proportional fines.Repeated game, Cartel, Oligopoly, Antitrust enforcement, Competition policy

Essays On Negotiation And Renegotiation

This dissertation consists of two essays related to negotiation and renegotiation in game theory. They investigate the renegotiation-proof equilibria in finitely repeated games and subgame perfect equilibria in negotiation games, respectively.;The renegotiation-proof equilibria in finitely repeated games with many players are studied in the first essay. Renegotiation-proof equilibrium requires not only subgame perfectness but also subgame efficiency. The main result of Benoi t and Krishna (1988) who studied the renegotiation-proof equilibria in two-player finitely repeated games does not apply to the games with more than two players. One sufficient condition for renegotiation-proof equilibria to be Pareto optimal in finitely repeated games with a sufficient long horizon is provided. An example shows that this sufficient condition cannot be weakened. The set of payoffs which can be approximated by renegotiation-proof equilibria in repeated games with a sufficiently long horizon is characterized such that it must be either Pareto optimal or dimensionally small . We also show by way of an example that renegotiation-proof equilibria may lead to very different outcomes even in the games whose stage games have identical sets of feasible and individually rational payoffs as well as identical Nash equilibria.;In the standard bargaining game of Rubinstein (1982), the disagreement payoff is independent of players\u27 past strategies. The model of negotiation proposed in the second essay merges ideas from bargaining theory and the repeated games literature. If no agreement has been reached in any period, players must play a stage game in normal form to determine that period payoffs. This model allows us to analyse the importance of strategic behaviour during periods without an agreement in the negotiations. The set of all perfect equilibria in the negotiation model is characterized. Quite generally, many feasible outcomes of the negotiation games can be sustained as subgame perfect equilibria. Particularly, many Pareto inefficient outcomes are sustainable even under the presence of perfect information and full rationality

Limit-order completion time in the London stock market

This study develops an econometric model of limit-order completion time using survival analysis. Time-to-completion for both buy and sell limit orders is estimated using tick-by-tick UK order data. The study investigates the explanatory power of variables that measure order characteristics and market conditions, such as the limitorder price, limit-order size, best bid-offer spread, and market volatility. The generic results show that limit-order completion time depends on some variables more than on others. This study also provides an investigation of how the dynamics of the market are incorporated into models of limit-order completion. The empirical results show that time-varying variables capture the state of an order book in a better way than static ones. Moreover, this study provides an examination of the prediction accuracy of the proposed models. In addition, this study provides an investigation of the intra-day pattern of order submission and time-of-day effects on limit-order completion time in the UK market. It provides evidence showing that limit orders placed in the afternoon period are expected to have the shortest completion times while orders placed in the mid-day period are expected to have the longest completion times, and the sensitivities of limit-order completion time to the explanatory variables vary over the trading day

Extreme Equilibria in a General Negotiation Model

We study a bargaining model with a disagreement game between o¤ers and countero¤ers. In order to characterize the set of its subgame perfect equilibrium payo¤s, we provide a recursive technique that relies on the Pareto frontier of equilibrium payo¤s. When players have di¤erent time preferences, reaching an immediate agreement may not be Pareto e ¢ cient. The recursive technique developed in this paper generalizes that of Shaked and Sutton (1984) by incorporating the possibility of making unacceptable proposals into the backward induction analysis. Results from this paper extend all the previous …ndings and resolve some open issues in the current literature