diff --git a/Makefile.am b/Makefile.am index e55a43a9b..e7b2c68c7 100644 --- a/Makefile.am +++ b/Makefile.am @@ -232,6 +232,11 @@ EXTRA_DIST = \ contrib/games/zero.nfg \ src/README.rst \ catalog/bagwell1995.efg \ + catalog/gilboa1997/fig2.efg \ + catalog/jakobsen2016/fig1a.efg \ + catalog/jakobsen2016/fig1b.efg \ + catalog/jakobsen2016/fig1c.efg \ + catalog/jakobsen2016/fig3.efg \ catalog/myerson1991/fig2_1.efg \ catalog/myerson1991/fig4_2.efg \ catalog/reiley2008/fig1.efg \ diff --git a/catalog/gilboa1997/fig2.efg b/catalog/gilboa1997/fig2.efg new file mode 100644 index 000000000..cf686fac8 --- /dev/null +++ b/catalog/gilboa1997/fig2.efg @@ -0,0 +1,19 @@ +EFG 2 R "Gilboa (1997) Two-Selves Absent-Minded Driver" { "Player 1" } +"A reformulation of the absent-minded driver problem from +`Gil97 `_ +using a multi-self approach. A chance move determines the order in which two selves act, +each facing a binary choice. Neither self knows the order of play, capturing absent-mindedness +through information sets that cross the chance branches rather than through imperfect recall. +" + +c "" 1 "" { "1" 1/2 "2" 1/2 } 0 +p "" 1 1 "" { "E" "B" } 0 +t "" 1 "Outcome 1" { 0 } +p "" 1 2 "" { "B" "E" } 0 +t "" 2 "Outcome 2" { 1 } +t "" 3 "Outcome 3" { 2 } +p "" 1 2 "" { "B" "E" } 0 +p "" 1 1 "" { "E" "B" } 0 +t "" 4 "Outcome 4" { 4 } +t "" 5 "Outcome 5" { 1 } +t "" 6 "Outcome 6" { 0 } diff --git a/catalog/jakobsen2016/fig1a.efg b/catalog/jakobsen2016/fig1a.efg new file mode 100644 index 000000000..a509ab4a7 --- /dev/null +++ b/catalog/jakobsen2016/fig1a.efg @@ -0,0 +1,23 @@ +EFG 2 R "Jakobsen, Sorensen, Conitzer (2016) Figure 1(a)" { "Player 1" "Player 2" } +"An example from `JakSorCon16 `_ illustrating a game +that is not exactly timeable. A coin toss determines which player moves first. +Each player guesses whether she went first, without distinguishing going first from going second. +Each player receives a payoff of 1 for a correct guess and 0 otherwise. +No deterministic or randomized timing can implement this game without leaking information. +" + +c "" 1 "" { "1" 1/2 "2" 1/2 } 0 +p "" 2 1 "" { "1" "2" } 0 +p "" 1 1 "" { "1" "2" } 0 +t "" 1 "Outcome 1" { 1, 0 } +t "" 2 "Outcome 2" { 0, 0 } +p "" 1 1 "" { "1" "2" } 0 +t "" 3 "Outcome 3" { 1, 1 } +t "" 4 "Outcome 4" { 0, 1 } +p "" 1 1 "" { "1" "2" } 0 +p "" 2 1 "" { "1" "2" } 0 +t "" 5 "Outcome 5" { 0, 1 } +t "" 6 "Outcome 6" { 0, 0 } +p "" 2 1 "" { "1" "2" } 0 +t "" 7 "Outcome 7" { 1, 1 } +t "" 8 "Outcome 8" { 1, 0 } diff --git a/catalog/jakobsen2016/fig1b.efg b/catalog/jakobsen2016/fig1b.efg new file mode 100644 index 000000000..c8ff21ab7 --- /dev/null +++ b/catalog/jakobsen2016/fig1b.efg @@ -0,0 +1,20 @@ +EFG 2 R "Jakobsen, Sorensen, Conitzer (2016) Figure 1(b)" { "Player 1" "Player 2" } +"An example from `JakSorCon16 `_ illustrating a game +that has an exact deterministic timing. A coin toss determines the flow of the game; +player 1 only plays if the coin comes up Heads, and if so plays first. +Player 2 always plays, but cannot distinguish whether the coin came up Heads or Tails. +Each player receives a payoff of 1 for a correct guess and 0 otherwise. +This game can be timed by letting player 1 play at time 1 and player 2 at time 2. +" + +c "" 1 "" { "1" 1/2 "2" 1/2 } 0 +p "" 2 1 "" { "1" "2" } 0 +t "" 1 "Outcome 1" { 0, 0 } +t "" 2 "Outcome 2" { 0, 1 } +p "" 1 1 "" { "1" "2" } 0 +p "" 2 1 "" { "1" "2" } 0 +t "" 3 "Outcome 3" { 0, 1 } +t "" 4 "Outcome 4" { 0, 0 } +p "" 2 1 "" { "1" "2" } 0 +t "" 5 "Outcome 5" { 1, 1 } +t "" 6 "Outcome 6" { 1, 0 } diff --git a/catalog/jakobsen2016/fig1c.efg b/catalog/jakobsen2016/fig1c.efg new file mode 100644 index 000000000..f72bf9284 --- /dev/null +++ b/catalog/jakobsen2016/fig1c.efg @@ -0,0 +1,19 @@ +EFG 2 R "Jakobsen, Sorensen, Conitzer (2016) Figure 1(c)" { "Player 1" "Player 2" } +"An example from `JakSorCon16 `_ illustrating a game +that is not exactly timeable. A coin toss determines the order of players. +The player moving second is only offered a bet if the player moving first guessed correctly. +Each player receives a payoff of 1 for a correct guess and 0 otherwise. +No deterministic or randomized timing can implement this game without leaking information. +" + +c "" 1 "" { "1" 1/2 "2" 1/2 } 0 +p "" 2 1 "" { "1" "2" } 0 +t "" 1 "Outcome 1" { 0, 0 } +p "" 1 1 "" { "1" "2" } 0 +t "" 2 "Outcome 2" { 1, 1 } +t "" 3 "Outcome 3" { 0, 1 } +p "" 1 1 "" { "1" "2" } 0 +t "" 4 "Outcome 4" { 0, 0 } +p "" 2 1 "" { "1" "2" } 0 +t "" 5 "Outcome 5" { 1, 1 } +t "" 6 "Outcome 6" { 1, 0 } diff --git a/catalog/jakobsen2016/fig3.efg b/catalog/jakobsen2016/fig3.efg new file mode 100644 index 000000000..1429f7481 --- /dev/null +++ b/catalog/jakobsen2016/fig3.efg @@ -0,0 +1,49 @@ +EFG 2 R "Jakobsen, Sorensen, Conitzer (2016) Figure 3" { "Player 1" "Player 2" "Player 3" "Player 4" } +"An example from `JakSorCon16 `_ illustrating +the extensive form of an onion routing game that is not exactly timeable. +Chance chooses a sender by drawing a signal from {0, 1, 2, 3} with equal probability. +The sender does not make a strategic choice; only the two intermediary players act. +For signal i: +(a) the sender is the player whose index (mod 4) equals i, +(b) the recipient is the player whose index (mod 4) equals i-1. +The first intermediary is Player i+2 (mod 4) and the second is Player i+1. +The full mapping is as follows: +Signal 0: Player 4 sends to Player 3. Player 2 acts first, then Player 1. +Signal 1: Player 1 sends to Player 4. Player 3 acts first, then Player 2. +Signal 2: Player 2 sends to Player 1. Player 4 acts first, then Player 3. +Signal 3: Player 3 sends to Player 2. Player 1 acts first, then Player 4. +Each player has one information set with two member nodes, that is, they cannot distinguish which position they are at. +Each intermediary chooses to either forward the envelope or obstruct by keeping it. +Each player wants to obstruct the protocol if they are the first intermediary, but wants to help if they are the second. +If both intermediaries forward, the message is delivered. +In that case, the first intermediary receives -1 and the second intermediary receives 1+epsilon. +All other players receive 0. +If either intermediary obstructs, the message is not delivered and all players receive 0. +With epsilon set to 0.01, the payoffs for successful delivery are: +Signal 0: (1.01, -1, 0, 0). +Signal 1: (0, 1.01, -1, 0). +Signal 2: (0, 0, 1.01, -1). +Signal 3: (-1, 0, 0, 1.01). +" + +c "" 1 "" { "0" 1/4 "1" 1/4 "2" 1/4 "3" 1/4 } 0 +p "" 2 1 "" { "1" "2" } 0 +t "" 1 "Outcome 1" { 0, 0, 0, 0 } +p "" 1 1 "" { "1" "2" } 0 +t "" 2 "Outcome 2" { 0, 0, 0, 0 } +t "" 3 "Outcome 3" { 1.01, -1, 0, 0 } +p "" 3 1 "" { "1" "2" } 0 +t "" 4 "Outcome 4" { 0, 0, 0, 0 } +p "" 2 1 "" { "1" "2" } 0 +t "" 5 "Outcome 5" { 0, 0, 0, 0 } +t "" 6 "Outcome 6" { 0, 1.01, -1, 0 } +p "" 4 1 "" { "1" "2" } 0 +t "" 7 "Outcome 7" { 0, 0, 0, 0 } +p "" 3 1 "" { "1" "2" } 0 +t "" 8 "Outcome 8" { 0, 0, 0, 0 } +t "" 9 "Outcome 9" { 0, 0, 1.01, -1 } +p "" 1 1 "" { "1" "2" } 0 +t "" 10 "Outcome 10" { 0, 0, 0, 0 } +p "" 4 1 "" { "1" "2" } 0 +t "" 11 "Outcome 11" { 0, 0, 0, 0 } +t "" 12 "Outcome 12" { -1, 0, 0, 1.01 } diff --git a/contrib/games/cross.efg b/contrib/games/cross.efg deleted file mode 100644 index bc3904794..000000000 --- a/contrib/games/cross.efg +++ /dev/null @@ -1,22 +0,0 @@ -EFG 2 R "Criss-crossing infosets" { "Player 1" "Player 2" } -"" - -p "ROOT" 1 1 "" { "1" "2" } 0 -p "" 2 1 "" { "1" "2" } 0 -p "" 1 2 "" { "1" "2" } 0 -p "" 2 2 "" { "1" "2" } 0 -t "" 0 -t "" 0 -t "" 0 -p "" 1 2 "" { "1" "2" } 0 -t "" 0 -t "" 0 -p "" 2 2 "" { "1" "2" } 0 -p "" 1 3 "" { "1" "2" } 0 -p "" 2 1 "" { "1" "2" } 0 -t "" 0 -t "" 0 -t "" 0 -p "" 1 3 "" { "1" "2" } 0 -t "" 0 -t "" 0 diff --git a/doc/biblio.rst b/doc/biblio.rst index ca292ffc4..b256f566b 100644 --- a/doc/biblio.rst +++ b/doc/biblio.rst @@ -93,6 +93,10 @@ General game theory articles and texts .. [Bag1995] Bagwell, K. 1995, 'Commitment and observability in games', *Games and Economic Behavior*, vol. 8, pp. 271-280. +.. [Gil97] Gilboa, I. 1997, + 'A Comment on the Absent-Minded Driver Paradox', + *Games and Economic Behavior*, vol. 20, pp. 25-30. + .. [Harsanyi1967a] Harsanyi, J. 1967, 'Games of incomplete information played by Bayesian players I', *Management Science*, vol. 14, pp. 159-182. @@ -105,6 +109,11 @@ General game theory articles and texts 'Games of incomplete information played by Bayesian players III', *Management Science*, vol. 14, pp. 486-502. +.. [JakSorCon16] Jakobsen, S. K, Sørensen, T. B. and Conitzer, V. 2016, + 'Timeability of Extensive-Form Games', + *Proceedings of the Seventh Innovations in Theoretical Computer Science Conference*, + pp. 191-199. + .. [KreWil82] Kreps, D. and Wilson, R. 1982, 'Sequential equilibria', *Econometrica*, vol. 50, pp. 863-894.