## Invited Session Fri.3.MA 043

#### Friday, 15:15 - 16:45 h, Room: MA 043

**Cluster 8: Game theory** [...]

### Analysis of equilibria in noncooperative games

**Chair: Marc Uetz**

**Friday, 15:15 - 15:40 h, Room: MA 043, Talk 1**

**Martin Hoefer**

Contribution games in networks

**Coauthor: Elliot Anshelevich**

**Abstract:**

Motivated by contribution scenarios in (social) networks, we analyze network contribution games in which each agent in a network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure success we use a reward function for each relationship. Every agent is trying to maximize the reward from all relationships that it is involved in. We consider pairwise equilibria of this game, and characterize the existence, computational complexity, and quality of equilibrium. Our results concern several natural classes of functions such as convex or concave rewards. We also discuss extensions towards altruistic behavior and different local reward sharing rules.

**Friday, 15:45 - 16:10 h, Room: MA 043, Talk 2**

**Tobias Harks**

Congestion games with variable demands

**Coauthor: Max Klimm**

**Abstract:**

We initiate the study of congestion games with variable

demands where the (variable) demand has to be assigned to exactly

one subset of resources. The players' incentives to use higher

demands are stimulated by non-decreasing and concave utility

functions. The payoff for a player is defined as the difference

between the utility of the demand and the associated cost

on the used resources. Although this class of non-cooperative

games captures many elements of real-world applications, it has not

been studied in this generality, to our knowledge, in the past.

We study the fundamental problem of the existence of pure Nash equilibria.

As our main result we give a complete characterizations of cost functions

that ensure the existence of at least one pure Nash equilibrium.

**Friday, 16:15 - 16:40 h, Room: MA 043, Talk 3**

**Jasper de Jong**

Decentralized mechanisms for throughput scheduling

**Abstract:**

Motivated by the organization of decentralized service systems, we study new models for throughput scheduling. In throughput scheduling, we have a set of jobs *i* with value *w*_{i}, processing requirement *p*_{i}, and deadline *d*_{i}, to be processed non-preemptively on a set of unrelated servers. The goal is to maximize the total value of jobs finished before their deadline. While several approximation algorithms with different performance guarantees exist for this and related models, we are interested in decentralized mechanisms where the servers act selfishly according to some given, simple protocol. We show by simple, combinatorial arguments that, when each server deploys an *α*-approximation locally, any Nash equilibrium still yields an *(α+1)*-approximation with respect to the global optimum. This bound is tight, even in the case of related machines, unit weights and unit processing times. For models with identical machines, the bound can be improved to *\frac{\sqrt[α]{e}}{\sqrt[α]{e}-1}*. Some of our results also extend to online models with corresponding competitive ratios.