Multi-Player Quantum Games

Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess a new form of equilibrium strategy, one which has no analogue either in traditional games or even in two-player quantum games. In these `pure' coherent equilibria, entanglement shared among multiple players enables new kinds of cooperative behavior: indeed it can act as a contract, in the sense that it prevents players from successfully betraying one-another.Comment: 5 pages, 2 figs. Substantial revisons inc. new result

An Analysis of the Quantum Penny Flip Game using Geometric Algebra

We analyze the quantum penny flip game using geometric algebra and so determine all possible unitary transformations which enable the player Q to implement a winning strategy. Geometric algebra provides a clear visual picture of the quantum game and its strategies, as well as providing a simple and direct derivation of the winning transformation, which we demonstrate can be parametrized by two angles. For comparison we derive the same general winning strategy by conventional means using density matrices.Comment: 8 Pages, 1 Figure, accepted for publication in the Journal of Physical Society of Japa

Sequential innovation, naked exclusion, and upfront lump-sum payments

We present a potentially benign naked exclusion mechanism that can be applied to sequential innovation; a non-patentable original innovation by the incumbent supplier fosters derivative innovation by rivals. In the absence of an appropriate legal framework, the original innovator’s equilibrium exclusivity contracts block subsequent efficient entry even if there is (leader-follower) competition in the contracting phase. However, the legal framework may maximize social welfare by imposing a ban on upfront lumps-sum payments in exclusivity contracts (by all suppliers) combined with an outright ban on exclusivity contracts by the derivative innovator. The former ban precludes the exclusion of socially beneficial derivative innovation by causing the incumbent supplier to resort to accommodation, rather than to pure exclusion, strategies. The latter ban complements the former by preventing inefficient or excessive derivative innovation

Quantum Matching Pennies Game

A quantum version of the Matching Pennies (MP) game is proposed that is played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct the quantum game without using the state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We embed the classical game within the quantum game such that the classical MP game results when the quantum mechanical joint probabilities become factorizable. We report new Nash equilibria in the quantum MP game that emerge when the quantum mechanical joint probabilities maximally violate the Clauser-Horne-Shimony-Holt form of Bell's inequality.Comment: Revised in light of referees' comments, submitted to Journal of the Physical Society of Japan, 14 pages, 1 figur

PERFECT RECALL AND PRUNING IN GAMES WITH IMPERFECT INFORMATION 1

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72986/1/j.1467-8640.1996.tb00256.x.pd

An integrative framework of preemption strategies

Pre-print; author's draftThis paper performs a review of the various pre-emption strategies prescribed in the economics literature. These are cost superiority, consumers' switching cost, channel exclusivity, environmental barriers of entry and credible commitment to react aggressively. Through our analysis, we develop an integrative framework of the pre-emption strategies that will result in long-term payoffs to the firm. The framework proposes that there are two key dimensions—strategic advantage and strategic focus—and identify five generic types of pre-emption strategies for market incumbents. These are the switching cost, blockade, credible commitment, tie-up, and cost leadership strategies. The pre-emption strategies and the framework presented can assist managerial decision-making for the successful pre-emption of potential competition to complement their existing efforts

Vertical integration, market foreclosure and quality investment

We study incentives to vertically integrate in an industry with verti- cally differentiated downstream firms. Vertical integration by one of the firms increases production costs for the rival. Increased production costs negatively affects quality investment both by the integrated firm and the unintegrated rival. Quality investment by both firms decreases under any (vertical inte- gration) scenario. The decrease in quality invesment by both firms softens competition among downstream firms. By integrating first, a firm always produces the high quality good and earns higher profits. A fully integrated industry, with increased product differentiation, is observed in equilibrium. Due to increase in firm profits, social welfare under this structure is greater than under no integration.info:eu-repo/semantics/publishedVersio

Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.Comment: 20 pages, no figure, revise