Dynamic Resource Allocation Games

Abstract

Abstract. In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it -we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability.

An Abstraction-Refinement Methodologyfor Reasoning about Network Games†

“…Closest to this work are works that apply ideas from formal verification to NGs. This includes an extension of NGs to objectives that are richer than reachability [37], NGs in which the players select their paths dynamically [52], reasoning about real-time in NGs [53,54], and efficient reasoning about NGs that are structured in a hierarchical manner [55]. The latter work is of special relevance, as it is motivated by the need to cope with large NGs.…”

Classifying Convergence Complexity of Nash Equilibria in Graphical Games Using Distributed Computing Theory

“…Game theory offers a natural approach to this issue in the form of multiplayer network games [14,30]. Be it resource allocation [5], routing [44], provision of public goods [30], virus inoculation [4], voting [46], or the spread of trends through social networks [1], instances of network games are everywhere to be found. They all have in common that interactions and players' decisions are in some way governed by the underlying graph and that players' payoffs usually depend on the network that links them.…”

The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

“…• Avni et al [5] study another variation of congestion games. The difference is that in their model, players make multiple, incremental decisions, and each time choose a single resource that extends the current solution.…”

“…In some sense, this model mixes sequential and simultaneous decision making, and the main results of [5] are on the existence and non-existence of (pure strategy) subgame perfect equilibria.…”

“…and that of the optimum remains arbitrarily close to 5. To this end consider the same instance but change the cost coefficient of arc (1, 2) from 2 to 2 + , that of arc (1, 5) from 4 to 4 + , and those of arcs(2,4) and(3,5) from 0 to .With the latter observation not only the sequential price of anarchy but also the sequential price of stability 4 equals 7/5 in the two-player case. This is because it is possible to prove a matching upper bound, even for the more general class of symmetric affine (not necessarily network) congestion games.…”