64:. In general, this random Chinese postman tour is indeed an optimal search strategy if and only if the graph consists of a set of Eulerian graphs connected in a tree-like structure. A misleadingly simple example of a graph not in this family consists of two nodes connected by three arcs. The random Chinese postman tour (equivalent to traversing the three arcs in a random order) is not optimal, and the optimal way to search these three arcs is complicated.
93:, i.e., finding a target on the infinite line, which has attracted much attention over several decades and has been analyzed as a search game. It has also been used to find a minimax trajectory for searching a set of concurrent rays. Optimal searching in the plane is performed by using exponential spirals. Searching a set of concurrent rays was later re-discovered in Computer Science literature as the 'cow-path problem'.
32:
radius and at this very moment capture occurs. The game is zero sum with the payoff being the time spent in searching. As mathematical models, search games can be applied to areas such as hide-and-seek games that children play or representations of some tactical military situations. The area of search games was introduced in the last chapter of
31:
called the search space. The searcher can choose any continuous trajectory subject to a maximal velocity constraint. It is always assumed that neither the searcher nor the hider has any knowledge about the movement of the other player until their distance apart is less than or equal to the discovery
88:
trajectory for problems of these types is always a geometric sequence (or exponential function for continuous problems). This result yields an easy method to find the minimax trajectory by minimizing over a single parameter (the generator of this sequence) instead of searching over the whole
237:
56:
A natural strategy to search for a stationary target in a graph (in which arcs have lengths) is to find a minimal closed curve L that covers all the arcs of the graph. (L is called a
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tour). Then, traverse L with probability 1/2 for each direction. This strategy seems to work well if the graph is
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M. Chrobak, A princess swimming in the fog looking for a monster cow, ACM Sigact news, 35(2), 74–78 (2004).
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Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
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In general, the reasonable framework for searching an unbounded domain, as in the case of an
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36:' classic book "Differential Games" and has been developed further by
737:
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162:"On the optimality of a simple strategy for searching graphs"
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89:trajectory space. This tool has been used for the
140:
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8:
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254:
246:
212:
177:
147:The Theory of Search Games and Rendezvous
195:"Yet More on the linear search problem"
101:
122:
120:
118:
84:in Computer Science literature). The
7:
193:Beck, Anatole; Newman, D.J. (1970).
166:International Journal of Game Theory
317:First-player and second-player win
14:
130:, Academic Press, New York (1980)
424:Coalition-proof Nash equilibrium
434:Evolutionarily stable strategy
112:, John Wiley and Sons, (1965),
1:
362:Simultaneous action selection
236:MY Kao, JH Reif and SR Tate,
200:Israel Journal of Mathematics
1299:List of games in game theory
474:Quantal response equilibrium
464:Perfect Bayesian equilibrium
399:Bayes correlated equilibrium
48:deals with a moving target.
768:Optional prisoner's dilemma
494:Self-confirming equilibrium
1356:
1233:Principal variation search
949:Aumann's agreement theorem
612:Strategy-stealing argument
519:Trembling hand equilibrium
449:Markov perfect equilibrium
444:Mertens-stable equilibrium
1269:Combinatorial game theory
928:Princess and monster game
479:Quasi-perfect equilibrium
404:Bayesian Nash equilibrium
76:, is to use a normalized
46:princess and monster game
1284:Evolutionary game theory
1017:Antoine Augustin Cournot
903:Guess 2/3 of the average
700:Strictly determined game
489:Satisfaction equilibrium
307:Escalation of commitment
16:Two-person zero-sum game
1289:Glossary of game theory
888:Stackelberg competition
509:Strong Nash equilibrium
27:which takes place in a
1314:Tragedy of the commons
1294:List of game theorists
1274:Confrontation analysis
984:Sprague–Grundy theorem
499:Sequential equilibrium
419:Correlated equilibrium
144:S. Alpern and S. Gal,
1335:Non-cooperative games
1087:Jean-François Mertens
179:10.1007/s001820000056
91:linear search problem
1216:Search optimizations
1092:Jennifer Tour Chayes
979:Revelation principle
974:Purification theorem
913:Nash bargaining game
878:Bertrand competition
863:El Farol Bar problem
828:Electronic mail game
793:Lewis signaling game
332:Hierarchy of beliefs
160:Gal, Shmuel (2001).
1264:Bounded rationality
883:Cournot competition
833:Rock paper scissors
808:Battle of the sexes
798:Volunteer's dilemma
670:Perfect information
597:Dominant strategies
429:Epsilon-equilibrium
312:Extensive-form game
1243:Paranoid algorithm
1223:Alpha–beta pruning
1102:John Maynard Smith
933:Rendezvous problem
773:Traveler's dilemma
763:Gift-exchange game
758:Prisoner's dilemma
675:Large Poisson game
642:Bargaining problem
542:Backward induction
514:Subgame perfection
469:Proper equilibrium
214:10.1007/BF02798690
150:, Springer (2003).
110:Differential Games
1340:Search algorithms
1322:
1321:
1228:Aspiration window
1197:Suzanne Scotchmer
1152:Oskar Morgenstern
1047:Donald B. Gillies
989:Zermelo's theorem
918:Induction puzzles
873:Fair cake-cutting
848:Public goods game
778:Coordination game
652:Intransitive game
577:Forward induction
459:Pareto efficiency
439:Gibbs equilibrium
409:Berge equilibrium
357:Simultaneous game
82:competitive ratio
68:Unbounded domains
1347:
1309:Topological game
1304:No-win situation
1202:Thomas Schelling
1182:Robert B. Wilson
1142:Merrill M. Flood
1112:John von Neumann
1022:Ariel Rubinstein
1007:Albert W. Tucker
858:War of attrition
818:Matching pennies
592:Pairing strategy
454:Nash equilibrium
377:Mechanism design
342:Normal-form game
297:Cooperative game
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74:online algorithm
23:is a two-person
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1238:max^n algorithm
1211:
1207:William Vickrey
1167:Reinhard Selten
1122:Kenneth Binmore
1037:David K. Levine
1032:Daniel Kahneman
999:
993:
969:Negamax theorem
959:Minimax theorem
937:
898:Diner's dilemma
753:All-pay auction
719:
705:Stochastic game
657:Mean-field game
628:
621:
587:Markov strategy
523:
389:
381:
352:Sequential game
337:Information set
322:Game complexity
292:Congestion game
280:
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58:Chinese postman
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1172:Robert Axelrod
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1159:
1154:
1149:
1147:Olga Bondareva
1144:
1139:
1137:Melvin Dresher
1134:
1129:
1127:Leonid Hurwicz
1124:
1119:
1114:
1109:
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1094:
1089:
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1074:
1069:
1064:
1062:Harold W. Kuhn
1059:
1054:
1052:Drew Fudenberg
1049:
1044:
1042:David M. Kreps
1039:
1034:
1029:
1027:Claude Shannon
1024:
1019:
1014:
1009:
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991:
986:
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964:Nash's theorem
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845:
840:
835:
830:
825:
823:Ultimatum game
820:
815:
810:
805:
803:Dollar auction
800:
795:
790:
788:Centipede game
785:
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755:
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745:
743:Infinite chess
740:
735:
729:
727:
721:
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718:
717:
712:
710:Symmetric game
707:
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697:
695:Signaling game
692:
690:Screening game
687:
682:
680:Potential game
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667:
659:
654:
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619:
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607:Mixed strategy
604:
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484:Risk dominance
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327:Graphical game
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207:(4): 419–429.
185:
172:(4): 533–542.
152:
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108:Rufus Isaacs,
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1257:Miscellaneous
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1200:
1198:
1195:
1193:
1192:Samuel Bowles
1190:
1188:
1187:Roger Myerson
1185:
1183:
1180:
1178:
1177:Robert Aumann
1175:
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1170:
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1132:Lloyd Shapley
1130:
1128:
1125:
1123:
1120:
1118:
1117:Kenneth Arrow
1115:
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1103:
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1098:
1097:John Harsanyi
1095:
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1075:
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1067:Herbert Simon
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869:
868:Fair division
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843:Dictator game
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715:Zero-sum game
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685:Repeated game
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603:
602:Pure strategy
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565:
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562:De-escalation
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504:Shapley value
502:
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372:Succinct game
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78:cost function
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43:
39:
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30:
26:
25:zero-sum game
22:
1162:Peyton Young
1157:Paul Milgrom
1072:Hervé Moulin
1012:Amos Tversky
954:Folk theorem
665:-player game
662:
582:Grim trigger
240:, SODA 1993.
232:
223:
204:
198:
188:
169:
165:
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145:
128:Search Games
127:
109:
104:
80:(called the
71:
55:
42:Steve Alpern
34:Rufus Isaacs
20:
18:
1279:Coopetition
1082:Jean Tirole
1077:John Conway
1057:Eric Maskin
853:Blotto game
838:Pirate game
647:Global game
617:Tit for tat
547:Bid shading
537:Appeasement
387:Equilibrium
367:Solved game
302:Determinacy
285:Definitions
278:game theory
21:search game
1329:Categories
923:Trust game
908:Kuhn poker
572:Escalation
567:Deterrence
557:Cheap talk
529:Strategies
347:Preference
276:Topics of
97:References
38:Shmuel Gal
1107:John Nash
813:Stag hunt
552:Collusion
1248:Lazy SMP
942:Theorems
893:Deadlock
748:Checkers
629:of games
391:concepts
126:S. Gal,
62:Eulerian
52:Strategy
1000:figures
783:Chicken
637:Auction
627:Classes
86:minimax
44:. The
738:Chess
725:Games
414:Core
40:and
998:Key
209:doi
174:doi
29:set
1331::
733:Go
203:.
197:.
170:29
168:.
164:.
135:^
117:^
19:A
663:n
269:e
262:t
255:v
217:.
211::
205:8
182:.
176::
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