Return full profiles from enumpoly_solve (#791)

Previously, for extensive games `enumpoly` returned "stub" profiles.  These profiles were in principle
extendable to Nash equilibria (although the check for doing so was not fully reliable).
However, having incomplete profiles raised a large number of practical issues computationally and
in terms of interpretation.

This change clarifies the operation of this method on extensive games.  Specifically, a given support of
actions is equivalent to specifying a given set of terminal nodes which may have positive probability.
A solution to the indifference conditions (in the sequence form) maps onto a probability distribution over
terminal nodes.  In order to confirm that such a probability distribution is implementable by a Nash
equilibrium, the method searches over all pure-action completions of the partial profile, and returns
the first such profile found.  In other words, for a given set of realisation-equivalent Nash equilibria, the
method returns a sample from that set.

Closes #660.

---------

Co-authored-by: Rahul Savani <rahul.savani@gmail.com>

Author: tturocy

Makefile.am

@@ -406,9 +406,6 @@ gambit_enumpoly_SOURCES = \
     src/solvers/enumpoly/polypartial.imp \
 	src/solvers/enumpoly/polysolver.cc \
 	src/solvers/enumpoly/polysolver.h \
-	src/solvers/enumpoly/polyfeasible.h \
-	src/solvers/enumpoly/behavextend.cc \
-	src/solvers/enumpoly/behavextend.h \
 	src/solvers/enumpoly/efgpoly.cc \
 	src/solvers/enumpoly/nfgpoly.cc \
 	src/solvers/enumpoly/enumpoly.h \

doc/tools.enumpoly.rst

@@ -24,6 +24,19 @@ supports which have the fewest strategies in total.  For many classes
 of games, this will tend to lower the average time until finding one equilibrium,
 as well as finding the second equilibrium (if one exists).
 
+For extensive games, a support of actions equates to allowing positive
+probabilities over a subset of terminal nodes.  The indifference conditions
+used are those for the sequence form defined on the projection of the game
+to that support of actions.  A solution to these equations implies a probability
+distribution over terminal nodes.  The algorithm then searches for
+a profile that is a Nash equilibrium that implements that probability
+distribution.  If there exists at least one such profile, a sample one is returned.
+Note that for probability distributions which assign zero probability to some terminal
+nodes, it is generally the case that there are (infinitely) many such profiles.
+Subsequent analysis of unreached information sets can yield alternative
+profiles that specify different choices at unreached information sets
+while still satisfying the Nash equilibrium conditions.
+
 When the verbose switch `-v` is used, the program outputs each support
 as it is considered. The supports are presented as a comma-separated
 list of binary strings, where each entry represents one player. The

src/games/behavmixed.cc

@@ -234,12 +234,12 @@ template <class T> MixedBehaviorProfile<T> MixedBehaviorProfile<T>::Normalize()
 template <class T> MixedBehaviorProfile<T> MixedBehaviorProfile<T>::ToFullSupport() const
 {
   CheckVersion();
-  MixedBehaviorProfile<T> full(GetGame());
+  MixedBehaviorProfile full(GetGame());
 
   for (auto player : m_support.GetGame()->GetPlayers()) {
     for (auto infoset : player->GetInfosets()) {
       for (auto action : infoset->GetActions()) {
-        full[action] = (m_support.Contains(action)) ? (*this)[action] : T(0);
+        full[action] = (m_support.Contains(action)) ? (*this)[action] : T{0};
       }
     }
   }

src/games/behavspt.cc

@@ -73,8 +73,10 @@ void BehaviorSupportProfile::AddAction(const GameAction &p_action)
   if (pos == support.end() || *pos != p_action) {
     // Action is not in the support at the infoset; add at this location to keep sorted by number
     support.insert(pos, p_action);
-    for (const auto &node : GetMembers(p_action->GetInfoset())) {
-      ActivateSubtree(node->GetChild(p_action));
+    for (const auto &node : p_action->GetInfoset()->GetMembers()) {
+      if (m_nonterminalReachable[node]) {
+        ActivateSubtree(node->GetChild(p_action));
+      }
     }
   }
 }
@@ -86,25 +88,16 @@ bool BehaviorSupportProfile::RemoveAction(const GameAction &p_action)
   auto pos = std::find(support.begin(), support.end(), p_action);
   if (pos != support.end()) {
     support.erase(pos);
-    for (const auto &node : GetMembers(p_action->GetInfoset())) {
-      DeactivateSubtree(node->GetChild(p_action));
+    for (const auto &node : p_action->GetInfoset()->GetMembers()) {
+      if (m_nonterminalReachable[node]) {
+        DeactivateSubtree(node->GetChild(p_action));
+      }
     }
     return !support.empty();
   }
   return false;
 }
 
-std::list<GameInfoset> BehaviorSupportProfile::GetInfosets(const GamePlayer &p_player) const
-{
-  std::list<GameInfoset> answer;
-  for (const auto &infoset : p_player->GetInfosets()) {
-    if (m_infosetReachable.at(infoset)) {
-      answer.push_back(infoset);
-    }
-  }
-  return answer;
-}
-
 bool BehaviorSupportProfile::HasReachableMembers(const GameInfoset &p_infoset) const
 {
   const auto &members = p_infoset->GetMembers();
@@ -150,17 +143,6 @@ void BehaviorSupportProfile::DeactivateSubtree(const GameNode &n)
   }
 }
 
-std::list<GameNode> BehaviorSupportProfile::GetMembers(const GameInfoset &p_infoset) const
-{
-  std::list<GameNode> answer;
-  for (const auto &member : p_infoset->GetMembers()) {
-    if (m_nonterminalReachable.at(member)) {
-      answer.push_back(member);
-    }
-  }
-  return answer;
-}
-
 //========================================================================
 //                 BehaviorSupportProfile: Sequence form
 //========================================================================

src/games/behavspt.h

@@ -130,20 +130,6 @@ class BehaviorSupportProfile {
   //@{
   /// Can the information set be reached under this support?
   bool IsReachable(const GameInfoset &p_infoset) const { return m_infosetReachable.at(p_infoset); }
-  /// Get the information sets for the player reachable under the support
-  std::list<GameInfoset> GetInfosets(const GamePlayer &) const;
-  /// Get the members of the information set reachable under the support
-  std::list<GameNode> GetMembers(const GameInfoset &) const;
-  //@}
-
-  /// @name Identification of dominated actions
-  //@{
-  /// Returns true if action 'a' is dominated by action 'b'
-  bool Dominates(const GameAction &a, const GameAction &b, bool p_strict) const;
-  /// Returns true if the action is dominated by some other action
-  bool IsDominated(const GameAction &a, bool p_strict) const;
-  /// Returns a copy of the support with dominated actions eliminated
-  BehaviorSupportProfile Undominated(bool p_strict) const;
   //@}
 
   class Infosets {