From 5da9ec4e1f1fd464ff74928815c8d81c702ba06f Mon Sep 17 00:00:00 2001 From: drdkad Date: Tue, 24 Mar 2026 22:32:25 +0000 Subject: [PATCH 1/8] Add Gilboa (1997) two-agents reformulation of absent-minded driver to catalog --- catalog/gilboa1997/fig2.efg | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 catalog/gilboa1997/fig2.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 } From 194cb311fc90c8f979c2bb52d34d6a6917931e14 Mon Sep 17 00:00:00 2001 From: drdkad Date: Tue, 24 Mar 2026 23:09:44 +0000 Subject: [PATCH 2/8] Add three games from Fig 1 in Jakobsen (2016) to catalog --- catalog/jakobsen2016/fig1a.efg | 23 +++++++++++++++++++++++ catalog/jakobsen2016/fig1b.efg | 20 ++++++++++++++++++++ catalog/jakobsen2016/fig1c.efg | 19 +++++++++++++++++++ 3 files changed, 62 insertions(+) create mode 100644 catalog/jakobsen2016/fig1a.efg create mode 100644 catalog/jakobsen2016/fig1b.efg create mode 100644 catalog/jakobsen2016/fig1c.efg 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 } From 82249743a1769f6abbc586974f8ba900b907a90d Mon Sep 17 00:00:00 2001 From: drdkad Date: Wed, 25 Mar 2026 09:01:09 +0000 Subject: [PATCH 3/8] Add the game from Fig 3 in Jakobsen (2016) to catalog --- catalog/jakobsen2016/fig3.efg | 49 +++++++++++++++++++++++++++++++++++ 1 file changed, 49 insertions(+) create mode 100644 catalog/jakobsen2016/fig3.efg diff --git a/catalog/jakobsen2016/fig3.efg b/catalog/jakobsen2016/fig3.efg new file mode 100644 index 000000000..8e39bf2c9 --- /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 } From 30ec655cb26e54036d9e218233aeb16dec47dd17 Mon Sep 17 00:00:00 2001 From: drdkad Date: Wed, 25 Mar 2026 09:01:25 +0000 Subject: [PATCH 4/8] Update bibliography --- doc/biblio.rst | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/doc/biblio.rst b/doc/biblio.rst index ca292ffc4..87948a83c 100644 --- a/doc/biblio.rst +++ b/doc/biblio.rst @@ -92,6 +92,12 @@ 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] Itzhak Gilboa, "A Comment on the Absent-Minded Driver Paradox", + 25-30, Games and Economic Behavior , 20, 1997. + +.. [Harsanyi1967a] John Harsanyi, "Games of Incomplete Information Played + By Bayesian Players I", 159-182, Management Science , 14, 1967. .. [Harsanyi1967a] Harsanyi, J. 1967, 'Games of incomplete information played by Bayesian players I', @@ -105,6 +111,13 @@ General game theory articles and texts 'Games of incomplete information played by Bayesian players III', *Management Science*, vol. 14, pp. 486-502. +.. [JakSorCon16] Sune K. Jakobsen, Troels B. Sørensen, and Vincent Conitzer, + "Timeability of Extensive-Form Games", 191-199, Proceedings of the + Seventh Innovations in Theoretical Computer Science Conference (ITCS) , 2016. + +.. [KreWil82] David Kreps and Robert Wilson, "Sequential Equilibria", + 863-894, Econometrica , 50, 1982. + .. [KreWil82] Kreps, D. and Wilson, R. 1982, 'Sequential equilibria', *Econometrica*, vol. 50, pp. 863-894. From 7b4d0e27635de5bfd8a6f44adb731a1faa85b91b Mon Sep 17 00:00:00 2001 From: drdkad Date: Wed, 25 Mar 2026 09:07:52 +0000 Subject: [PATCH 5/8] Update Makefile.am --- Makefile.am | 5 +++++ 1 file changed, 5 insertions(+) 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 \ From f05758dbca2b4887f9fb1cce247c088099a4b305 Mon Sep 17 00:00:00 2001 From: drdkad Date: Wed, 25 Mar 2026 10:38:47 +0000 Subject: [PATCH 6/8] fix typo --- catalog/jakobsen2016/fig3.efg | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/catalog/jakobsen2016/fig3.efg b/catalog/jakobsen2016/fig3.efg index 8e39bf2c9..1429f7481 100644 --- a/catalog/jakobsen2016/fig3.efg +++ b/catalog/jakobsen2016/fig3.efg @@ -5,7 +5,7 @@ Chance chooses a sender by drawing a signal from {0, 1, 2, 3} with equal probabi 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. +(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. From 44c340962acabb29900747254d66acef826031ad Mon Sep 17 00:00:00 2001 From: drdkad Date: Wed, 25 Mar 2026 10:39:23 +0000 Subject: [PATCH 7/8] Resolve conflicts in bibliography --- doc/biblio.rst | 18 +++++++----------- 1 file changed, 7 insertions(+), 11 deletions(-) diff --git a/doc/biblio.rst b/doc/biblio.rst index 87948a83c..b256f566b 100644 --- a/doc/biblio.rst +++ b/doc/biblio.rst @@ -92,12 +92,10 @@ 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] Itzhak Gilboa, "A Comment on the Absent-Minded Driver Paradox", - 25-30, Games and Economic Behavior , 20, 1997. -.. [Harsanyi1967a] John Harsanyi, "Games of Incomplete Information Played - By Bayesian Players I", 159-182, Management Science , 14, 1967. +.. [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', @@ -111,12 +109,10 @@ General game theory articles and texts 'Games of incomplete information played by Bayesian players III', *Management Science*, vol. 14, pp. 486-502. -.. [JakSorCon16] Sune K. Jakobsen, Troels B. Sørensen, and Vincent Conitzer, - "Timeability of Extensive-Form Games", 191-199, Proceedings of the - Seventh Innovations in Theoretical Computer Science Conference (ITCS) , 2016. - -.. [KreWil82] David Kreps and Robert Wilson, "Sequential Equilibria", - 863-894, Econometrica , 50, 1982. +.. [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. From abb2330bb9b013ae9914b4a74450f96a19b8d620 Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Wed, 25 Mar 2026 10:48:07 +0000 Subject: [PATCH 8/8] Deleting cross.efg as it is superseded by the new examples. --- contrib/games/cross.efg | 22 ---------------------- 1 file changed, 22 deletions(-) delete mode 100644 contrib/games/cross.efg 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