The game to play: expanding the co-opetition proposal through the strategic games matrix

Purpose - Using Brandenburger and Nalebuff`s 1995 co-opetition model as a reference, the purpose of this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enable scholars and managers to identify which games may be played in response to the different conflict of interest situations faced by companies in their business environments. Design/methodology/approach - The literature on game theory and business strategy are reviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel games are described and modeled. Findings - The co-opetition model is not sufficient to realistically represent most of the conflict of interest situations faced by companies. It seeks to address this problem through development of the SGM, which expands upon Brandenburger and Nalebuff`s model by providing a broader perspective, through incorporation of an additional dimension (power ratio between players) and three novel, respectively, (rival, individualistic, and associative). Practical implications - This proposed model, based on the concepts of game theory, should be used to train decision- and policy-makers to better understand, interpret and formulate conflict management strategies. Originality/value - A practical and original tool to use game models in conflict of interest situations is generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on the SGM to suggest in which situations they Could be useful. Two innovative games are described to fit four different types of conflict situations that so far have no corresponding game in the literature. A test application of the SGM to a classic Intel Corporation strategic management case, in the complex personal computer industry, shows that the proposed method is able to describe, to interpret, to analyze, and to prescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.

A note on the multiple partners assignment game

In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International journal of Game Theory 1, 11-130] agents are allowed to form one partnership at most. That paper proves that, in the context of firms and workers, given two stable payoffs for the firms there is a stable payoff which gives each firm the larger of the two amounts and also one which gives each of them the smaller amount. Analogous result applies to the workers. Sotomayor [Sotomayor, M., 1992. The multiple partners game. In: Majumdar, M. (Ed.), Dynamics and Equilibrium: Essays in Honor to D. Gale. Mcmillian, pp. 322-336] extends this analysis to the case where both types of agents may form more than one partnership and an agent`s payoff is multi-dimensional. Instead, this note concentrates in the total payoff of the agents. It is then proved the rather unexpected result that again the maximum of any pair of stable payoffs for the firms is stable but the minimum need not be, even if we restrict the multiplicity of partnerships to one of the sides. (C) 2009 Elsevier B.V. All rights reserved.

Adjusting prices in the multiple-partners assignment game

Starting with an initial price vector, prices are adjusted in order to eliminate the excess demand and at the same time to keep the transfers to the sellers as low as possible. In each step of the auction, to which set of sellers should those transfers be made is the key issue in the description of the algorithm. We assume additively separable utilities and introduce a novel distinction by considering multiple sellers owing multiple identical objects and multiple buyers with an exogenously defined quota, consuming more than one object but at most one unit of a seller`s good and having multi-dimensional payoffs. This distinction induces a necessarily more complicated construction of the over-demanded sets than the constructions of these sets for the other assignment games. For this approach, our mechanism yields the buyer-optimal competitive equilibrium payoff, which equals the buyer-optimal stable payoff. The symmetry of the model allows to getting the seller-optimal stable payoff and the seller-optimal competitive equilibrium payoff can then be also derived.

Prospective randomized trial of EUS versus ERCP-guided common bile duct stone removal: an interim report (with video)

Background: EUS is being increasingly utilized for the diagnosis of choledocholithiasis and microlithiasis, especially in patients with biliary colic. Simultaneously, there is also a rising interest in the use of EUS for therapeutic interventions. Objectives: Our goal was to assess the effectiveness of EUS-directed common bile duct (CBD) stone removal to compare its safety and effectiveness with ERCP-directed intervention. Design: interim results of a prospective, randomized, single-center blinded clinical trial. Setting: A single tertiary care referral center. Patients: Fifty-two patients with uncomplicated CBD stones were prospectively randomized to CBD cannulation and stone removal under EUS or ERCP guidance. Main Outcome Measurements and Interventions: Primary outcome measure was the rate of successful cannulation of the CBD. Secondary Outcome measures included Successful removal of stones and overall complication rates. Results: CBD cannulation followed by stone extraction was successful in 23 of 26 patients (88.5%) in the EUS group (1) versus 25 of 26 patients (96.2%) in the ERCP group (11) (95% CI, -27.65%, 9.88%). Overall, there were 3 complications in the EUS group and 4 complications in the ERCP group. Limitation: The current study is an interim report from a single center report and performed by a single operator. Conclusions: Our preliminary analysis indicates that Outcomes following EUS-guided CBD stone retrieval are equivalent to those following ERCP EUS-related adverse events are similar to those following ERCP. ERCP and EUS-guided stone retrieval appears to be equally effective for therapeutic interventions of the bile duct. Additional studies are required to validate these preliminary results and to determine predictors of success of EUS-guided stone removal. (Gastrointest Endosc 2009;69:238-43.)