### Table 4. Average payoff of a single player with a minority strategy when it played against the other 99 players with a majority strategy.

"... In PAGE 24: ... Such evaluation was performed for all combinations of the six strategies. Simulation results are summarized in Table4 . From this table, we can see that the performance of the optimal strategy for the previous actions strongly depends on the strategy of the other 99 players.... In PAGE 24: ...verage payoff was very small (i.e., 47.2). This strategy, however, can play very well against the other strategies. Actually, high average payoff was obtained from this strategy in Table4 when the other 99 players adopted another strategy. We can observe similar characteristic features in the simulation results by the fuzzy rule-based classification strategy in Table 4 Table 4.... In PAGE 24: ...Table4... ..."

### Table 3. Average payoff from each strategy when all the players used the same strategy.

"... In PAGE 23: ...1 Competition between two strategies We have already examined the performance of each strategy by computer simulations where a single strategy was adopted by all the 100 players. Table3 summarizes the average payoff obtained from each strategy in such computer simulations. In this table, good results were obtained from the maximum expected payoff strategy and the fuzzy rule-based approximation strategy.... In PAGE 23: ...2 when the average payoff was maximized by genetic algorithms (see [11]). From the comparison of Table3 with these results, we can see that the results by the maximum expected payoff strategy and the fuzzy rule-based approximation strategy are very good. Table 3.... In PAGE 24: ...ombinations of the six strategies. Simulation results are summarized in Table 4. From this table, we can see that the performance of the optimal strategy for the previous actions strongly depends on the strategy of the other 99 players. When the other 99 players also used this strategy (see Table3 ), the average payoff was very small (i.... ..."

### Table 3. Utility function of strategies and player Ui(x)

"... In PAGE 12: .... (5) establishing groundwater regulation. Combining these actions, we have indenti ed the set of strategies given in Table 2. If we let Table3 represent the players apos; utilities at a certain time period in the negotiation process, then we can compute values of Qi(x; t) using equation (6). The results are given in Table 4.... ..."

### Table 3. Utility function of strategies and player Ui(x)

"... In PAGE 9: .... (5) establishing groundwater regulation. Combining these actions, we have indenti ed the set of strategies given in Table 2. If we let Table3 represent the players apos; utilities at a certain time period in the negotiation process, then we can compute values of Qi(x; t) using equation (6). The results are given in Table 4.... ..."

### Table 3. Utility function of strategies and player Ui(x)

"... In PAGE 12: .... (5) establishing groundwater regulation. Combining these actions, we have indenti ed the set of strategies given in Table 2. If we let Table3 represent the players apos; utilities at a certain time period in the negotiation process, then we can compute values of Qi(x; t) using equation (6). The results are given in Table 4.... ..."

### Table 1: Strategy ranking based on tournament.

"... In PAGE 3: ...Table 1: Strategy ranking based on tournament. Table1 , the player using the strategy of Saby wins the tour- nament, followed closely by a player using best response to fictitious play. In the table, we show the average score per iteration to show the average level of preferences obtained.... ..."

### Table 1: Functional evaluation strategies

1999

"... In PAGE 4: ...Table 1: Functional evaluation strategies An overview of the properties of common evaluation strategies is given in Table1 . In the literature, the terms used are not generally agreed upon.... ..."

Cited by 2

### Table 8. Frequently used fuzzy if-then rules by Player 1 in the competition among the six strategies.

"... In PAGE 26: ... In the same manner as in the previous subsection, we monitored the winner rule in the fuzzy rule-based classification strategy and the fuzzy reasoning process in the fuzzy rule-based approximation strategy. Final fuzzy if-then rules after the 1000th round are summarized in Table8 and Table 9. In these tables, all the trained fuzzy if-then rules insisted that Market 5 should be chosen by ... ..."

### Table 5. Frequently used fuzzy if-then rules by Player 1 during the game-playing against the other 99 players with the optimal strategy for the previous actions.

"... In PAGE 25: ...-24- manner as in Section 4. Table5 shows frequently used fuzzy if-then rules when Player 1 with the fuzzy rule-based classification strategy played against the other 99 players with the optimal strategy for the previous actions. From the fuzzy if-then rules in Table 5, we can see that the fuzzy rule-based classification system learned the market selection knowledge that can make use of the synchronized oscillation of selected markets.... In PAGE 25: ... Table 5 shows frequently used fuzzy if-then rules when Player 1 with the fuzzy rule-based classification strategy played against the other 99 players with the optimal strategy for the previous actions. From the fuzzy if-then rules in Table5 , we can see that the fuzzy rule-based classification system learned the market selection knowledge that can make use of the synchronized oscillation of selected markets. The trained fuzzy rule-based classification system chooses Market 3 when the previous market prices at Market 3 and Market 5 were low and high respectively.... In PAGE 25: ... Player 1 with the trained fuzzy rule-based approximation systems in Table 6 chooses a market with a lower previous market price between Market 3 and Market 5. As shown in Table5 and Table 6, the two fuzzy rule-based strategies learned the same market selection knowledge through different learning schemes. ... In PAGE 29: ...-28- player. The final fuzzy rule-based classification system after the 1000th round was almost the same as Table5 in Subsection 6.1.... ..."

### Table 2. Number of Players on Teams that were Surveyed

"... In PAGE 13: ... The purpose of economic impact studies is to measure the economic return to residents. The difference between the two approaches is illustrated in Table2 which shows that on a typical financial balance sheet, a park and recreation agency would report a return of $7,000 from the softball tournament. However, if the agency used an economic balance sheet, as tourism agencies do, then it would show a $50,000 return.... In PAGE 13: ... This is the more appropriate measure because it is residents in the jurisdiction who paid the capital and operating costs of the softball complex, and it is the residents who receive the new dollars that come into the community from visitors participating in the tournament. If the capital cost of the softball complex was $1 million, then the investment would pay for itself after 20 tournaments ( Table2 ). (Assuming that no operational expenses were incurred for the tournament beyond those required for normal maintenance).... ..."