diff --git a/spot/twaalgos/game.cc b/spot/twaalgos/game.cc
index df259b84a..17f94a7e4 100644
--- a/spot/twaalgos/game.cc
+++ b/spot/twaalgos/game.cc
@@ -1056,7 +1056,18 @@ namespace spot
     (*owners)[state] = owner;
   }
 
-  const region_t& get_state_players(const_twa_graph_ptr arena)
+  const region_t& get_state_players(const const_twa_graph_ptr& arena)
+  {
+    region_t *owners = arena->get_named_prop<region_t>
+      ("state-player");
+    if (!owners)
+      throw std::runtime_error
+        ("get_state_players(): state-player property not defined, not a game?");
+
+    return *owners;
+  }
+
+  const region_t& get_state_players(twa_graph_ptr& arena)
   {
     region_t *owners = arena->get_named_prop<region_t>
       ("state-player");
@@ -1081,7 +1092,7 @@ namespace spot
   }
 
 
-  const strategy_t& get_strategy(const_twa_graph_ptr arena)
+  const strategy_t& get_strategy(const const_twa_graph_ptr& arena)
   {
     auto strat_ptr = arena->get_named_prop<strategy_t>("strategy");
     if (!strat_ptr)
@@ -1174,7 +1185,7 @@ namespace spot
     (*winners)[state] = winner;
   }
 
-  const region_t& get_state_winners(const_twa_graph_ptr arena)
+  const region_t& get_state_winners(const const_twa_graph_ptr& arena)
   {
     region_t *winners = arena->get_named_prop<region_t>("state-winner");
     if (!winners)
diff --git a/spot/twaalgos/game.hh b/spot/twaalgos/game.hh
index df5d27439..dbaccce75 100644
--- a/spot/twaalgos/game.hh
+++ b/spot/twaalgos/game.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2017-2022 Laboratoire de Recherche et Développement
+// Copyright (C) 2017-2023 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -163,14 +163,18 @@ namespace spot
 
   /// \ingroup games
   /// \brief Get the owner of all states
+  ///@{
   SPOT_API
-  const region_t& get_state_players(const_twa_graph_ptr arena);
+  const region_t& get_state_players(const const_twa_graph_ptr& arena);
+  SPOT_API
+  const region_t& get_state_players(twa_graph_ptr& arena);
+  ///@}
 
   /// \ingroup games
   /// \brief Get or set the strategy
   /// @{
   SPOT_API
-  const strategy_t& get_strategy(const_twa_graph_ptr arena);
+  const strategy_t& get_strategy(const const_twa_graph_ptr& arena);
   SPOT_API
   void set_strategy(twa_graph_ptr arena, const strategy_t& strat);
   SPOT_API
@@ -214,5 +218,5 @@ namespace spot
   /// \ingroup games
   /// \brief Get the winner of all states
   SPOT_API
-  const region_t& get_state_winners(const_twa_graph_ptr arena);
+  const region_t& get_state_winners(const const_twa_graph_ptr& arena);
 }
diff --git a/spot/twaalgos/mealy_machine.cc b/spot/twaalgos/mealy_machine.cc
index e2b1523de..25bab05a9 100644
--- a/spot/twaalgos/mealy_machine.cc
+++ b/spot/twaalgos/mealy_machine.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2021, 2022 Laboratoire de Recherche et Développement
+// Copyright (C) 2021, 2022, 2023 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -3995,7 +3995,7 @@ namespace
 
     // 0 -> "Env" next is input props
     // 1 -> "Player" next is output prop
-    const auto& spref = get_state_players(mmw);
+    const region_t& spref = get_state_players(mmw);
     assert((spref.size() == mmw->num_states())
            && "Inconsistent state players");
 
@@ -4146,9 +4146,9 @@ namespace spot
     const unsigned initl = left->get_init_state_number();
     const unsigned initr = right->get_init_state_number();
 
-    auto& spr = get_state_players(right);
+    const region_t& spr = get_state_players(right);
 #ifndef NDEBUG
-    auto& spl = get_state_players(left);
+    const region_t& spl = get_state_players(left);
     // todo
     auto check_out = [](const const_twa_graph_ptr& aut,
                         const auto& sp)
diff --git a/spot/twaalgos/synthesis.cc b/spot/twaalgos/synthesis.cc
index 4e38efd5b..aef11d27b 100644
--- a/spot/twaalgos/synthesis.cc
+++ b/spot/twaalgos/synthesis.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2020-2022 Laboratoire de Recherche et
+// Copyright (C) 2020-2023 Laboratoire de Recherche et
 // Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -138,12 +138,12 @@ namespace{
   // Note, this only deals with deterministic strategies
   // Note, assumes that env starts playing
   twa_graph_ptr
-  apply_strategy(const twa_graph_ptr& arena,
+  apply_strategy(const const_twa_graph_ptr& arena,
                  bool unsplit, bool keep_acc)
   {
-    const auto& win = get_state_winners(arena);
-    const auto& strat = get_strategy(arena);
-    const auto& sp = get_state_players(arena);
+    const region_t& win = get_state_winners(arena);
+    const strategy_t& strat = get_strategy(arena);
+    const region_t& sp = get_state_players(arena);
     auto outs = get_synthesis_outputs(arena);
 
     if (!win[arena->get_init_state_number()])
@@ -1955,7 +1955,7 @@ namespace spot
       throw std::runtime_error("arena is null.");
     auto& arena_r = *arena;
 
-    const auto& sp = get_state_players(arena);
+    const region_t& sp = get_state_players(arena);
     bdd all_ap = arena->ap_vars();
 
     if (std::find_if(arena->ap().cbegin(), arena->ap().cend(),