Some of the seminal papers by Henkin and Lorenzen, and some of the papers cited below, appear in the collection Infinitistic Methods (Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 2–9 September, 1959), Oxford: Pergamon Press, 1961. The editors are unnamed.

Games in the History of Logic

• Dutilh Novaes, Catarina, 2007, Formalizing Medieval Logical Theories: Suppositio, Consequentiae and Obligationes, New York: Springer-Verlag. (Scholar)
• Hamblin, Charles, 1970, Fallacies, London: Methuen. (Scholar)
• Hilbert, David, 1967, “Die Grundlagen der Mathematik”, translated as “The foundations of mathematics,” in Jean van Heijenoort (ed.), From Frege to Gödel, Cambridge Mass.: Harvard University Press, pp. 464–479. (Scholar)
• Paul of Venice, Logica Magna II (8), Tractatus de Obligationibus, E. Jennifer Ashworth (ed.), New York: British Academy and Oxford University Press, 1988.
• Weyl, Hermann, 1925–7, “Die heutige Erkenntnislage in der Mathematik,”, translated as “The current epistemological situation in mathematics” in Paolo Mancosu, From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s, New York: Oxford University Press, 1988, pp. 123–142. (Scholar)
• Zermelo, Ernst, 1913, “Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels,” in E. W. Hobson and A. E. H. Love (eds.), Proceedings of the Fifth International Congress of Mathematicians, Volume II, Cambridge: Cambridge University Press. (Scholar)

Games for Teaching Logic

• Barwise, Jon and John Etchemendy, 1995, The Language of First-Order Logic, including Tarski’s World 3.0, Cambridge: Cambridge University Press. (Scholar)
• Carroll, Lewis, 1887, The Game of Logic, London: Macmillan. (Scholar)
• Dienes, Zoltan P., and E. W. Golding, 1966, Learning Logic, Logical Games, Harlow: Educational Supply Association. (Scholar)
• Havas, Katalin, 1999, “Learning to think: Logic for children,” in Proceedings of the Twentieth World Congress of Philosophy (Volume 3: Philosophy of Education), David M. Steiner (ed.), Bowling Green Ohio: Bowling Green State University Philosophy, pp. 11–19. (Scholar)
• Nifo, Agostino, 1521, Dialectica Ludicra (Logic as a game), Florence: Bindonis. (Scholar)
• Weng, Jui-Feng, with Shian-Shyong Tseng and Tsung-Ju Lee, 2010, “Teaching Boolean logic through game rule tuning,” IEEE Transactions, Learning Technologies, 3(4): 319–328. [Uses Pac-Man games to teach Boolean logic to junior high school students.] (Scholar)

Logical Games

• Gale, David and F. M. Stewart, 1953, “Infinite games with perfect information,” in Contributions to the Theory of Games II (Annals of Mathematics Studies 28), H. W. Kuhn and A. W. Tucker (eds.), Princeton: Princeton University Press, pp. 245–266. (Scholar)
• Kechris, Alexander S., 1995, Classical Descriptive Set Theory, New York: Springer-Verlag. (Scholar)
• Marion, Mathieu, 2009, “Why play logical games?,” in Ondrej Majer, Ahti-Veikko Pietarinen, and Tero Tulenheimo eds., Games: Unifying Logic, Language and Philosophy, New York: Springer-Verlag, pp. 3-25. (Scholar)
• Osbourne, Martin J. and Ariel Rubinstein, 1994, A Course in Game Theory, Cambridge: MIT Press. (Scholar)
• Väänänen, Jouko, 2011, Models and Games, Cambridge: Cambridge University Press. (Scholar)
• van Benthem, Johan, 2011, Logical dynamics of information and interaction, Cambridge: Cambridge University Press, 2011. (Scholar)
• –––, 2014, Logic in games, Cambridge, MA: MIT Press. (Scholar)

Semantic Games for Classical Logic

• Henkin, Leon, 1961, “Some remarks on infinitely long formulas,” in Infinitistic Methods, op. cit., pp. 167–183. (Scholar)
• Hintikka, Jaakko, 1973, Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic, Oxford: Clarendon Press. (Scholar)
• Hintikka, Jaakko, 1996, The Principles of Mathematics Revisited, New York: Cambridge University Press. [See for example pages 40, 82 on the axiom of choice.] (Scholar)
• Hodges, Wilfrid, 2001, “Elementary Predicate Logic 25: Skolem Functions,” in Dov Gabbay, and Franz Guenthner (eds.), Handbook of Philosophical Logic I, 2nd edition, Dordrecht: Kluwer, pp. 86–91. [Proof of equivalence of game and Tarski semantics.] (Scholar)
• Kolaitis, Ph. G., 1985, “Game quantification,” in J. Barwise and S. Feferman (eds.), Model-Theoretic Logics, New York: Springer-Verlag, pp. 365-421. (Scholar)
• Peirce, Charles Sanders, 1898, Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898, ed. Kenneth Laine Ketner, Cambridge Mass., Harvard University Press, 1992. (Scholar)

Semantic Games with Imperfect Information

• Hintikka, Jaakko and Gabriel Sandu, 1997, “Game-theoretical semantics,” in Johan van Benthem and Alice ter Meulen (eds.), Handbook of Logic and Language, Amsterdam: Elsevier, pp. 361–410. (Scholar)
• Hodges, Wilfrid, 1997, “Compositional semantics for a language of imperfect information,” Logic Journal of the IGPL, 5: 539–563. (Scholar)
• Janssen, Theo M. V. and Francien Dechesne, 2006, “Signalling: a tricky business,” in J. van Benthem et al. (eds.), The Age of Alternative Logics: Assessing the Philosophy of Logic and Mathematics Today, Dordrecht: Kluwer, pp. 223–242. (Scholar)
• Mann, Allen L., Gabriel Sandu, and Merlin Sevenster, 2011, Independence-Friendly Logic: A Game-Theoretic Approach (London Mathematical Society Lecture Note Series 386), Cambridge: Cambridge University Press. (Scholar)
• von Neumann, John and Oskar Morgenstern, 1944, Theory of Games and Economic Behavior, Princeton: Princeton University Press. (Scholar)
• Väänänen, Jouko, 2007, Dependence Logic: A New Approach to Independence Friendly Logic, Cambridge: Cambridge University Press. (Scholar)

Semantic Games for Other Logics

• Bradfield, Julian and Colin Stirling, 2006, “Modal mu-calculi,” in P. Blackburn et al. (eds.), Handbook of Modal Logic, Amsterdam: Elsevier, pp. 721–756. (Scholar)
• Dekker, Paul, and Marc Pauly (eds.), 2002, Journal of Logic, Language and Information, 11(3): 287–387. [Special issue on Logic and Games.] (Scholar)
• Hennessy, Matthew, and Robin Milner, 1985, “Algebraic laws for indeterminism and concurrency,” Journal of the ACM, 32: 137–162. (Scholar)
• Parikh, Rohit, 1985, “The logic of games and its applications,” in Marek Karpinski and Jan van Leeuwen (eds.), “Topics in the Theory of Computation,” Annals of Discrete Mathematics, 24: 111–140. (Scholar)
• Pauly, Marc, and Rohit Parikh (eds.), 2003, Studia Logica, 72(2): 163–256 [Special issue on Game Logic.] (Scholar)
• Stirling, Colin, 2001, Modal and Temporal Properties of Processes, New York: Springer-Verlag. (Scholar)
• van Benthem, Johan, 2006, “The epistemic logic of IF games,” in Randall Auxier and Lewis Hahn (eds.), The Philosophy of Jaakko Hintikka, Chicago: Open Court pp. 481–513. (Scholar)
• van Benthem, Johan with Amitabha Gupta and Rohit Parikh, 2011, Proof, Computation and Agency, Dordrecht: Springer-Verlag. (Scholar)

Back-and-Forth Games

• Blackburn, Patrick with Maarten de Rijke and Yde Venema, 2001, Modal Logic, Cambridge: Cambridge University Press. (Scholar)
• Doets, Kees, 1996, Basic Model Theory, Stanford: CSLI Publications and FoLLI. (Scholar)
• Ebbinghaus, Heinz-Dieter and Jörg Flum, 1999, Finite Model Theory, 2nd edition, New York: Springer. (Scholar)
• Ehrenfeucht, Andrzej, 1961, “An application of games to the completeness problem for formalized theories,” Fundamenta Mathematicae, 49: 129–141. (Scholar)
• Grädel, Erich with Phokion G. Kolaitis, Leonid Libkin, Maarten Marx, Joel Spencer, Moshe Y. Vardi, Yde Venema, and Scott Weinstein, 2007, Finite Model Theory, Berlin: Springer-Verlag. (Scholar)
• Libkin, Leonid, 2004, Elements of Finite Model Theory, Berlin, Springer-Verlag. (Scholar)
• Otto, Martin, 1997, Bounded Variable Logics and Counting—A Study in Finite Models (Lecture Notes in Logic, 9), Berlin: Springer-Verlag. (Scholar)
• Peters, Stanley and Dag Westerståhl, 2006, Quantifiers in Language and Logic, Oxford: Clarendon Press. (Scholar)
• Tarski, Alfred, 1946, “Address at the Princeton University Bicentennial Conference on Problems of Mathematics (December 17–19, 1946),” Hourya Sinaceur (ed.), Bulletin of Symbolic Logic, 6 (2000): 1–44. (Scholar)
• van Benthem, Johan, 2001, “Correspondence Theory,” in Dov Gabbay and Franz Guenthner (eds.), Handbook of Philosophical Logic III, 2nd edition, Dordrecht: Kluwer. (Scholar)

Other Model-Theoretic Games

• Anthony, Martin, and Norman Biggs, 1992, Computational Learning Theory, Cambridge: Cambridge University Press. [For Vapnik-Chervonenkis dimension.] (Scholar)
• Gurevich, Yuri and Leo Harrington, 1984,“Trees, automata, and games,” in H. R. Lewis (ed.), Proceedings of the ACM Symposium on the Theory of Computing, San Francisco: ACM, pp. 171–182. (Scholar)
• Hirsch, Robin and Ian Hodkinson, 2002, Relation Algebras by Games, New York: North-Holland. (Scholar)
• Hodges, Wilfrid, 1985, Building Models by Games, Cambridge: Cambridge University Press. (Scholar)
• Hodges, Wilfrid, 1993, Model Theory, Cambridge: Cambridge University Press. (Scholar)
• Oxtoby, J. C., 1971, Measure and Category, New York: Springer-Verlag. (Scholar)
• Ziegler, Martin, 1980, “Algebraisch abgeschlossene Gruppen,” in S. I. Adian et al. (eds.), Word Problems II: The Oxford Book, Amsterdam: North-Holland, pp. 449–576. (Scholar)

Games of Dialogue, Communication and Proof

• Abramsky, Samson and Radha Jagadeesan, 1994, “Games and full completeness for multiplicative linear logic,” Journal of Symbolic Logic, 59: 543–574. (Scholar)
• Abramsky, Samson and Paul-André Melliès, 1999, “Concurrent games and full completeness,” in Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Science Press of the IEEE, pp. 431–442. (Scholar)
• Bench-Capon, T. J. M. and Paul E. Dunne, 2007, “Argumentation in artificial intelligence,” Artificial Intelligence, 171: 619–641. [The introduction to a rich collection of papers on the same theme on pages 642–937.] (Scholar)
• Blass, Andreas, 1992, “A game semantics for linear logic,” Annals of Pure and Applied Logic, 56: 183–220.
• Cignoli, Roberto L. O., Itala M. L. D’Ottaviano, and Daniele Mundici, 2000, Algebraic Foundations of Many-Valued Reasoning, Dordrecht: Kluwer. (Scholar)
• Felscher, Walter, 2001, “Dialogues as a foundation for intuitionistic logic,” in Dov Gabbay and Franz Guenthner (eds.), Handbook of Philosophical Logic V, 2nd edition, Dordrecht: Kluwer. (Scholar)
• Hodges, Wilfrid and Erik C. W. Krabbe, 2001, “Dialogue foundations,” Proceedings of the Aristotelian Society (Supplementary Volume), 75: 17–49. (Scholar)
• Japaridze, Giorgi, 2003, “Introduction to computability logic,” Annals of Pure and Applied Logic, 123: 1–99. (Scholar)
• Lorenzen, Paul, 1961 “Ein dialogisches Konstruktivitätskriterium,” in Infinitistic Methods, op. cit., 1961, pp. 193–200. (Scholar)
• Pudlak, Pavel, 2000, “Proofs as games,” American Mathematical Monthly, 107(6): 541–550. (Scholar)
• Walton, Douglas N. and Erik C. W. Krabbe, 1995, Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning, Albany: State University of New York Press. (Scholar)