### Table 1. Payoffs and probabilities for the game

2004

"... In PAGE 2: ...at the same time then this is a disaster because they will not get many more customers than usual but they will receive much less money per customer. An example of the possible payoffs is shown in Table1 , where the first number of each pair is the payoff of the row player and the second is that of the column player. The state with the highest average income (per store) is the one in which neither offers a sale.... In PAGE 4: ... Correlated equilibrium payoffs can be outside the convex hull of Nash equilibrium payoffs. For example, consider the game in Table1 . We first show that the probabilities given in the table produce a correlated equilibrium.... In PAGE 5: ...Furthermore, a correlated equilibrium with a non-uniform distribution can give a strictly higher average payoff than any with a uniform distribution in the same game. For example, in the game in Table1 , the uniform distribution over (Sale; Sale); (Sale; No Sale); (No Sale; Sale) also gives a correlated equilibrium, but this has an average payoff of (5 + 12 + 9)=3 = 82 3 which is lower than the 8 8 11 achieved with the non-uniform distribution in the table. It is interesting to wonder what happens for an arbitrary game when the trusted party is allowed to send more informative messages, rather than just informing each player of the action it is supposed to take.... In PAGE 6: ... In both protocols, the longest message is a list sent in the first step. For example, for the game in Table1 our protocol uses a list of length d11=3e = 4 while the one in [DHR00] uses one of length l.... ..."

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### Table 2. Mean investment levels No-trade payoff OO-game TP-game

"... In PAGE 13: ... In the TP-game average investment levels increase when the no-trade payoff increases. Evidence for this result is obtained from Table2 , which reports mean investment levels by bargaining game and no-trade payoff. Statistical tests are based on the average investment levels of individuals (rather than on separate investment decisions).... In PAGE 15: ... Result 3: Average investment levels are higher under the TP-game than under the OO-game. Support for Result 3 is again provided in Table2 . For given levels of the no-trade payoffs, the average investment levels of individuals are higher under the TP-game than under the OO-game.... In PAGE 30: ... Table A0 gives the mean individual investment levels together with the theoretical predictions. This is the analog of Table2 in the current paper. For both bargaining treatments we find the investment level to be (virtually) constant in the value of the no-trade payoff.... In PAGE 30: ... The single exception is the OO-treatment with r=7800 for which it is predicted that the investment level equals the socially efficient level. It is interesting to compare the results of Table A0 with the results of Table2 in the main text. For both bargaining situations, there is no significant difference between the mean investment levels in both tables for no-trade payoffs equal to 1800.... ..."

### Table 2. Results for Game 1

in Contents

2003

"... In PAGE 76: ... At the moment, we prefera fast set implementationwhich is more efficient and faster than the usual appropiateJava structures. Let us take a look at a few resultsin Table2 . Basedon a CHRapproach [22] we developed some boolean constraints for the solution of random 3-SAT- problems, i.... In PAGE 77: ...31 18.31 Table2 . A benchmarksetshowstheprogressfromsimpleBTto heuristicassistedCBJ.... In PAGE 77: ... The yes-instanceswere ne- glected, because the labelling algorithm aborts processing, as soon as it finds the solution.In Table2 one can see the comparisonbetween BT and CBJ for all no-instanceswith 50 variables.The comparisonconcernsthe number of jumps neededby an algorithmto process a problem.... In PAGE 93: ...square X1,4 X1,5 X1,6 X1,7 X2,1 square X2,3 X2,4 X2,5 square X2,7 X3,1 X3,2 X3,3 square X3,5 X3,6 X3,7 X4,1 X4,2 X4,3 square square X4,6 square square X5,2 X5,3 X5,4 X5,5 square X5,7 X6,1 X6,2 X6,3 square X6,5 X6,6 X6,7 X7,1 X7,2 square X7,4 X7,5 X7,6 X7,7 Table 1. A model for 7x7 grid Thresholdfor Time word2 word3 word4 word5 3 70 240 510 45ms 8 30 50 10 280ms 1 5 300 10 11ms 3 6 400 10 16ms 1 5 200 10 120ms fd relation 53ms Table2 . Some resultsfor 7x7 grid Thresholdfor Time word2 word3 word4 word5 3 70 240 310 380ms 3 30 80 200 gt;15min 3 70 240 410 58ms 3 70 260 410 76ms 3 65 240 410 78ms fd relation 102ms Table 3.... ..."

### Table 2: Payoff matrix for Allocation Game.

2001

"... In PAGE 4: ... They agree to flip a fair coin, and if it lands heads up, CGBD will choose the office and CGBE will choose the laboratory, with the opposite happening if it lands tails. Table2 illustrates the payoff matrix for these games. The utilities for each of these games are obtained in accordance with... ..."

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### Table 1: The payoff table for the backgammon game

"... In PAGE 7: ... 11 A player received payoffs at the end of a game. The payoffs were as shown in Table1 . If the losing side has borne off at least one checker, the rewards for the winner and the loser will be 0.... In PAGE 11: ...4 468.2 Table1 0: The performance of the members of the best team and the best team as a whole. The numbers shown are the distances achieved.... In PAGE 11: ...2 621.2 Table1 1: The performance of the members of the worst team and the worst team as a whole. The numbers shown are the distances achieved.... ..."

### Table 1. Game Generators in GAMUT

2004

"... In PAGE 7: ...2. They are listed in Table1 . While the in- ternal representations and algorithms used vary depend- ing on the set of games being generated, all of them must be able to return the number of players, the number of ac- tions for each player, and the payoff for a each player for any action profile.... ..."

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### Table 1. Game Generators in GAMUT

2004

"... In PAGE 7: ...2. They are listed in Table1 . While the in- ternal representations and algorithms used vary depend- ing on the set of games being generated, all of them must be able to return the number of players, the number of ac- tions for each player, and the payoff for a each player for any action profile.... ..."

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### Table 1. Game Generators in GAMUT

2004

"... In PAGE 7: ...2. They are listed in Table1 . While the in- ternal representations and algorithms used vary depend- ing on the set of games being generated, all of them must be able to return the number of players, the number of ac- tions for each player, and the payoff for a each player for any action profile.... ..."

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### Table 1. Game Generators in GAMUT

### Table 1: Various mechanisms as special cases of the parameterized payoff function in Equation 1. Note that the bargaining game, being asymmetric, is described by two payoff functions. These games are discussed in Section 5.

2004

"... In PAGE 2: ... This parameterized payoff function captures many known mechanisms. Table1 shows the parameter settings for sev- eral such games. Given a game description in this form, we search for Bayes- Nash equilibria through a straightforward iterative process.... In PAGE 5: ... 5 Examples Here we consider existing and new games and show that our method for finding best responses can confirm or re- discover known results as well as find previously unknown equilibria. There are many games not analyzed here to which our ap- proach is amenable, such as the All-Pay auction (both win- ner and loser pay their bids; encoded in Table1 ), incom- plete information versions of Cournot or Bertrand games, the War of Attrition (both winner and loser pay the second highest price), and voluntary participation games (agents choose an amount to contribute for a joint good and receive utility based on the sum of both contributions; encoded in Table 1). Our approach is not needed for incentive com- patible mechanisms such as the Vickrey auction, but, re- assuringly, our algorithm returns the dominant strategy of truthful bidding as a best response to any other strategy in that domain.... In PAGE 5: ... 5 Examples Here we consider existing and new games and show that our method for finding best responses can confirm or re- discover known results as well as find previously unknown equilibria. There are many games not analyzed here to which our ap- proach is amenable, such as the All-Pay auction (both win- ner and loser pay their bids; encoded in Table 1), incom- plete information versions of Cournot or Bertrand games, the War of Attrition (both winner and loser pay the second highest price), and voluntary participation games (agents choose an amount to contribute for a joint good and receive utility based on the sum of both contributions; encoded in Table1 ). Our approach is not needed for incentive com- patible mechanisms such as the Vickrey auction, but, re- assuringly, our algorithm returns the dominant strategy of truthful bidding as a best response to any other strategy in that domain.... ..."

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