First draft of a script to create (symmetric) two-player Bayesian games.

contrib/src/bayesgame/bayesgame.py

@@ -0,0 +1,70 @@
+"""Experimental script to build a two-player Bayesian game in an
+explicit extensive representation.
+"""
+import typing
+
+import pygambit as gbt
+
+
+def terminal_nodes(game: gbt.Game) -> list:
+    return [n for n in game.nodes() if n.is_terminal]
+
+
+def history(node: gbt.Node) -> list:
+    hist = []
+    while node.parent:
+        hist = [node.prior_action.label] + hist
+        node = node.parent
+    return hist
+
+
+def bayesian_game(types: list, actions: list,
+                  payoffs: typing.Callable) -> gbt.Game:
+    g = gbt.Game.new_tree(players=["Player 1", "Player 2"],
+                          title="Untitled Bayesian game")
+
+    g.append_move(g.root, g.players.chance, types)
+    g.append_move(g.root.children, g.players.chance, types)
+    g.append_move(terminal_nodes(g), g.players["Player 1"], actions)
+    g.reveal(g.root.infoset, g.players["Player 1"])
+    g.append_move(terminal_nodes(g), g.players["Player 2"], actions)
+    g.reveal(g.root.children[0].infoset, g.players["Player 2"])
+    for node in terminal_nodes(g):
+        g.set_outcome(node, g.add_outcome())
+        node.outcome["Player 1"], node.outcome["Player 2"] = payoffs(history(node))
+    return g
+
+
+def bach_stravinsky(hist: list):
+    """Bayesian game version of 'Bach or Stravinsky', from
+    Osborne and Rubenstein (1994), A course in game theory, exercise 27.1.
+    """
+    t1, t2, a1, a2 = hist
+    if a1 != a2:
+        return 0, 0
+    return (2 if a1 == t1.lower() else 1,
+            2 if a2 == t2.lower() else 1)
+
+
+def fp_pv_auction(hist: list) -> tuple:
+    """First-price private-values auction.
+    """
+    t1, t2, a1, a2 = [gbt.Decimal(v) for v in hist]
+    if a1 > a2:
+        return t1 - a1, 0
+    if a2 > a1:
+        return 0, t2 - a2
+    return (t1 - a1) / 2, (t2 - a2) / 2
+
+
+if __name__ == "__main__":
+    low_v = bayesian_game(["0", "2", "4", "6", "8", "11"],
+                          ["0", "1", "2", "3", "4", "5", "6"],
+                          fp_pv_auction)
+    high_v = bayesian_game(["0", "3", "5", "7", "9", "12"],
+                           ["0", "1", "2", "3", "4", "5", "6"],
+                           fp_pv_auction)
+    with open("low_v.efg", "w") as f:
+        f.write(low_v.write())
+    with open("high_v.efg", "w") as f:
+        f.write(high_v.write())