### Table 1: Price of anarchy of pure equilibria for linear latencies (left) and polynomial latencies of degree p (right).

in The

"... In PAGE 2: ... We also study both symmetric and asymmetric games. Our results (both lower and upper bounds) are summarized in the left part of Table1 . For the case of asymmetric games, the values hold also for network congestion games.... ..."

### TABLE VII THE PRICE OF ANARCHY

2007

Cited by 2

### Table 1. SUM MAX

in The

"... In PAGE 2: ... We also study both symmetric and asymmetric games. Our results (both lower and upper bounds) are summarized in the left part of Table1 . For the case of asymmetric games, the values hold also for network congestion games.... In PAGE 2: ...SUM MAX Symmetric p (p) p (p) Asymmetric p (p) (Np=(p+1)); O(N) Table1 : Price of anarchy of pure equilibria for linear latencies (left) and polynomial latencies of degree p (right). We also extend our results on the average social cost to the case of mixed Nash equilibria (with price of anarchy at most 2:619).... ..."

### Table 7.Growth of Cooperative Networks.

### Table 1: Characteristics of Equilibria of the Games

"... In PAGE 4: ... By #5Cgood quot; outcomes, we shall mean outcomes in which as many as possible of these features are present. In Table1 we show the extent to which these features are presentin the equilibria of the three games we consider. Payo#0B e#0Eciency is de#0Cned as the sum of row and column player payo#0Bs, normalized so that the maximum possible jointpayo#0B in a given game has an e#0Eciency of one and the minimum possible jointpayo#0B has an e#0Eciency of zero.... In PAGE 16: ... The round#7Bby#7Bround observed relative frequencies of cooperation are shown in Figure 2. Also shown are the average frequency of cooperation, at the far rightofeachbox, and the frequency of cooperation in each Nash equilibrium, as a horizontal line marked by an #5Cx quot; #28see also Table1 #29. Consistent with many repeated Prisoner apos;s Dilemma experiments, cooperation decreases over time #28toward the equilibrium level of zero#29 in all three PD cells.... ..."

### Table 1: A simple cooperative game reward function.

"... In PAGE 1: ... Upon execution of their actions all agents receive the reward that corresponds to the joint action. For example, Table1 describes the re- ward function for a simple cooperative single-stage game. If agent 1 executes action CQ and agent 2 executes action CP, the reward they receive is 5.... In PAGE 5: ... CP CQ CR CP 212 0 3 CQ 0 12 289 CR 0 0 381 Table 9: Results with exponential temperature. CP CQ CR CP 0 0 0 CQ 0 1000 0 CR 0 0 0 Table1 0: Results with optimistic assumption. CP CQ CR CP 988 0 0 CQ 0 4 0 CR 0 7 1 Table 11: Results with the FMQ heuristic.... In PAGE 5: ... CP CQ CR CP 0 0 0 CQ 0 1000 0 CR 0 0 0 Table 10: Results with optimistic assumption. CP CQ CR CP 988 0 0 CQ 0 4 0 CR 0 7 1 Table1 1: Results with the FMQ heuristic. 5 Discussion The FMQ heuristic performs equally well in the partially stochastic climbing game and the original deterministic climbing game.... In PAGE 5: ... The reward function for the stochastic climbing game is included in Table 12. Agent 1 CP CQ CR CP 10/12 5/-65 8/-8 Agent 2 CQ 5/-65 14/0 12/0 CR 5/-5 5/-5 10/0 Table1 2: The stochastic climbing game table (50%). It is obvious why the optimistic assumption fails to solve the fully stochastic climbing game.... ..."

### Table 1: A simple cooperative game reward function.

"... In PAGE 1: ... In multi-stage stochastic games, the execu- tion of a joint action yields not only a common reward but also the transition of the agents to a new state. Table1... ..."

### Table I. Cooperation Rates Key: Non-Terminal Periods, Terminal Periodsa

### Table 1: Characteristics of Equilibria of the Games Game Equilibrium Prob(Cooperation) Prob(Coordination) E ciency

"... In PAGE 4: ... By \good quot; outcomes, we shall mean outcomes in which as many as possible of these features are present. In Table1 we show the extent to which these features are present in the equilibria of the three games we consider. Payo e ciency is de ned as the sum of row and column player payo s, normalized so that the maximum possible joint payo in a given game has an e ciency of one and the minimum possible joint payo has an e ciency of zero.... ..."