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Perfect information
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<h2 id="examples">Examples</h2> <p><a href="/facts/Chess/47ykvkHF">Chess</a> is an example of a game with perfect information, as each player can see all the pieces on the board at all times.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> Other games with perfect information include <a href="/facts/Tic-tac-toe/EcwN1Rab">tic-tac-toe</a>, <a href="/facts/Reversi/Bxp4jHAw">Reversi</a>, <a href="/facts/Draughts/zrzKMsyu">checkers</a>, and <a href="/facts/Go_(game)/1fKhemww">Go</a>.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> </p><p>Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with chance, <i>but no secret information</i>, and games with <a href="/facts/Simultaneous_game/TkHcpJUo"><i>simultaneous moves</i></a> are games of perfect information.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a><a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a><a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> </p><p>Games which are <a href="/facts/Sequential_game/kFPCl6VN">sequential</a> (players alternate in moving) and which have <a href="/facts/Move_by_nature/flbEnjxq">chance events</a> (with known probabilities to all players) but <i>no secret information</i>, are sometimes considered games of perfect information. This includes games such as <a href="/facts/Backgammon/53mgqvtv">backgammon</a> and <a href="/facts/Monopoly_(game)/7r2PLNJY">Monopoly</a>. However, some academic papers do not regard such games as games of perfect information because the results of chance themselves are unknown prior to them occurring.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a><a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a><a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a><a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> </p><p>Games with <i>simultaneous moves</i> are generally not considered games of perfect information. This is because each player holds information, which is secret, and must play a move without knowing the opponent's secret information. Nevertheless, some such games are <a href="/facts/Symmetric_game/0mYUMxLN">symmetrical</a>, and fair. An example of a game in this category includes <a href="/facts/Rock_paper_scissors/mkUcl9Nv">rock paper scissors</a>.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a><a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a><a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a><a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Extensive_form_game/Yw9gQ7um">Extensive form game</a></li> <li><a href="/facts/Information_asymmetry/Tr9cgSk5">Information asymmetry</a></li> <li><a href="/facts/Dispersed_knowledge/upJNcw81">Partial knowledge</a></li> <li><a href="/facts/Screening_game/gKq37UUo">Screening game</a></li> <li><a href="/facts/Signaling_game/rl5ynxH7">Signaling game</a></li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Fudenberg, D. and <a href="/facts/Jean_Tirole/cIu3pK0t">Tirole, J.</a> (1993) <i>Game Theory</i>, <a href="/facts/MIT_Press/eTerUM3c">MIT Press</a>. (see Chapter 3, sect 2.2)</li> <li>Gibbons, R. (1992) <i>A primer in game theory</i>, Harvester-Wheatsheaf. (see Chapter 2)</li> <li><a href="/facts/R._Duncan_Luce/QSJFYkIM">Luce, R.D.</a> and <a href="/facts/Howard_Raiffa/HSPQtv7y">Raiffa, H.</a> (1957) <i>Games and Decisions: Introduction and Critical Survey</i>, Wiley & Sons (see Chapter 3, section 2)</li> <li><a href="https://mises.org/library/economics-groundhog-day">The Economics of <i>Groundhog Day</i></a> by economist D.W. MacKenzie, using the 1993 film <i><a href="/facts/Groundhog_Day_(film)/4py9df0n">Groundhog Day</a></i> to argue that perfect information, and therefore perfect competition, is impossible.</li> <li>Watson, J. (2013) <i>Strategy: An Introduction to Game Theory</i>, W.W. Norton and Co.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Osborne, M. J.; Rubinstein, A. (1994). "Chapter 6: Extensive Games with Perfect Information". A Course in Game Theory. Cambridge, Massachusetts: The MIT Press. ISBN 0-262-65040-1. <a href="0-262-65040-1" target="_blank">0-262-65040-1</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Khomskii, Yurii (2010). "Infinite Games (section 1.1)" (PDF). <a href="https://www.math.uni-hamburg.de/home/khomskii/infinitegames2010/Infinite%20Games%20Sofia.pdf" target="_blank">https://www.math.uni-hamburg.de/home/khomskii/infinitegames2010/Infinite%20Games%20Sofia.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Archived at Ghostarchive and the Wayback Machine: "Infinite Chess". PBS Infinite Series. March 2, 2017. Perfect information defined at 0:25, with academic sources arXiv:1302.4377 and arXiv:1510.08155 . <a href="https://ghostarchive.org/varchive/youtube/20211211/PN-I6u-AxMg" target="_blank">https://ghostarchive.org/varchive/youtube/20211211/PN-I6u-AxMg</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Mycielski, Jan (1992). "Games with Perfect Information". Handbook of Game Theory with Economic Applications. Vol. 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. ISBN 978-0-444-88098-7. <a href="978-0-444-88098-7" target="_blank">978-0-444-88098-7</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Thomas, L. C. (2003). Games, Theory and Applications. Mineola New York: Dover Publications. p. 19. ISBN 0-486-43237-8. <a href="0-486-43237-8" target="_blank">0-486-43237-8</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Osborne, M. J.; Rubinstein, A. (1994). "Chapter 11: Extensive Games with Imperfect Information". A Course in Game Theory. Cambridge Massachusetts: The MIT Press. ISBN 0-262-65040-1. <a href="0-262-65040-1" target="_blank">0-262-65040-1</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Khomskii, Yurii (2010). "Infinite Games (section 1.1)" (PDF). <a href="https://www.math.uni-hamburg.de/home/khomskii/infinitegames2010/Infinite%20Games%20Sofia.pdf" target="_blank">https://www.math.uni-hamburg.de/home/khomskii/infinitegames2010/Infinite%20Games%20Sofia.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Archived at Ghostarchive and the Wayback Machine: "Infinite Chess". PBS Infinite Series. March 2, 2017. Perfect information defined at 0:25, with academic sources arXiv:1302.4377 and arXiv:1510.08155 . <a href="https://ghostarchive.org/varchive/youtube/20211211/PN-I6u-AxMg" target="_blank">https://ghostarchive.org/varchive/youtube/20211211/PN-I6u-AxMg</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Mycielski, Jan (1992). "Games with Perfect Information". Handbook of Game Theory with Economic Applications. Vol. 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. ISBN 978-0-444-88098-7. <a href="978-0-444-88098-7" target="_blank">978-0-444-88098-7</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Janet Chen; Su-I Lu; Dan Vekhter. "Game Theory: Rock, Paper, Scissors". cs.stanford.edu. <a href="https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html" target="_blank">https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Ferguson, Thomas S. "Game Theory" (PDF). UCLA Department of Mathematics. pp. 56–57. <a href="/wiki/Thomas_S._Ferguson" target="_blank">/wiki/Thomas_S._Ferguson</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Burch; Johanson; Bowling. "Solving Imperfect Information Games Using Decomposition". Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence. <a href="https://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/viewFile/8407/8476" target="_blank">https://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/viewFile/8407/8476</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Mycielski, Jan (1992). "Games with Perfect Information". Handbook of Game Theory with Economic Applications. Vol. 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. ISBN 978-0-444-88098-7. <a href="978-0-444-88098-7" target="_blank">978-0-444-88098-7</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Janet Chen; Su-I Lu; Dan Vekhter. "Game Theory: Rock, Paper, Scissors". cs.stanford.edu. <a href="https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html" target="_blank">https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Ferguson, Thomas S. "Game Theory" (PDF). UCLA Department of Mathematics. pp. 56–57. <a href="/wiki/Thomas_S._Ferguson" target="_blank">/wiki/Thomas_S._Ferguson</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Burch; Johanson; Bowling. "Solving Imperfect Information Games Using Decomposition". Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence. <a href="https://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/viewFile/8407/8476" target="_blank">https://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/viewFile/8407/8476</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Mycielski, Jan (1992). "Games with Perfect Information". Handbook of Game Theory with Economic Applications. Vol. 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. ISBN 978-0-444-88098-7. <a href="978-0-444-88098-7" target="_blank">978-0-444-88098-7</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Janet Chen; Su-I Lu; Dan Vekhter. "Game Theory: Rock, Paper, Scissors". cs.stanford.edu. <a href="https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html" target="_blank">https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>Ferguson, Thomas S. "Game Theory" (PDF). UCLA Department of Mathematics. pp. 56–57. <a href="/wiki/Thomas_S._Ferguson" target="_blank">/wiki/Thomas_S._Ferguson</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>Burch; Johanson; Bowling. "Solving Imperfect Information Games Using Decomposition". Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence. <a href="https://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/viewFile/8407/8476" target="_blank">https://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/viewFile/8407/8476</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> </ol>