International Game Theory Review

There are numerous situations in which variability reduction is desirable. We examine cases where such reductions can be achieved by cooperating agents who share similar interests. Our goal is to quantify the contribution of each of the agents toward this reduction. We model this situation as a cooperative game in which the cost is defined as the minimal standard deviation the cooperating agents can achieve. We show that this game is subadditive and has a nonempty core. We derive special presentations for the Shapley and Banzhaf values.

This paper analyzes the strategic interaction between a crowdfunding platform specialized in medical projects and a set of potential investors. The problem is cast as a two-stage game. In the first stage, the platform chooses its participation fee and selects a project. In the second stage, investors decide whether to back the project or not. We consider a crowdfunding platform which runs all-or-nothing programs and transfers funds to the entrepreneur only if an investment target is reached. Moreover, we assume that some agents present a systematic positive bias driven by positive emotions about projects with high social impact, which is a major characteristic of medical projects. We frame the second-stage investor problem as a typical global game and solve it for the threshold equilibrium. The analysis reveals that crowdfunding finance might back financially inefficient projects, a result amplified by the existence of enthusiastic investors. We further show that the optimal fee charged by the platform is related to the frequency of overoptimistic agents, a result that might explain why platforms tend to over-emphasize the social role of their projects.

Generalizations of reactive and semi-reactive bargaining sets of TU games are defined for the case when objections and counter-objections are permitted not between singletons but between elements of a family of coalitions ${𝒜}$ and can use coalitions from ${ℬ}\supset {𝒜}$. Necessary and sufficient conditions on ${𝒜}$, ${ℬ}$ that ensure existence results for generalizations of the reactive bargaining set and of the semi-reactive barganing set at each TU game $(N,v)$ with nonnegative values are obtained. The existence conditions for the generalized reactive bargaining set do not coincide with existence conditions for the generalized kernel and coincide with conditions for the generalized semi-reactive bargaining set only if $\left|N\right|\le 4$ and ${ℬ}=2^N$. The conditions for the generalized semi-reactive bargaining set coincide with conditions for the generalized classical bargaining set that were described in the previous papers of the author.

For monotonic ${ℬ}$, the condition on ${𝒜}$ for existence of the generalized semi-reactive bargaining sets on the class of games with nonnegative values is also necessary and sufficient on the class of simple games, but similar result for the generalized classical bargaining sets is proved only for $\left|N\right|\le 6$.

Dynamic asymmetric contest games are examined under the assumption that the assessed value of the prize by each agent depends on the total effort of all agents, and each agent has only delayed information about the efforts of the competitors. Assuming gradient dynamics with continuous time scales, first the resulting one-delay model is investigated. Then, assuming additional delayed information about the agents’ own efforts, a two-delay model is constructed and analyzed. In both cases, first the characteristic equation is derived in the general case, and then two special cases are considered. First, symmetric agents are assumed and then general duopolies are examined. Conditions are derived for the local stability of the equilibrium including stability thresholds and stability switching curves.

An experiment was conducted on a sample of $500$ randomly generated symmetric bimatrix games with size $12$ and $15$. Distribution of support sizes and Nash equilibria are used to formulate a conjecture: for finding a symmetric NEP it is enough to check supports up to size $4$ whereas for nonsymmetric and all NEPs this number is $3$ and $2$, respectively. If true, this enables us to use a Las Vegas algorithm that finds a Nash equilibrium in polynomial time with high probability.

When an outside innovating firm has a cost-reducing technology, it can sell licenses of its technology to incumbent firms, or enter the market and at the same time sell licenses, or enter the market without license. We examine the definitions of license fees in such situations under oligopoly, one outside innovating firm and several incumbent firms, considering threat by entry by the innovating firm using a two-step auction.