Dynamic Coalitions in Games on Graphs with Preferences over Temporal Goals

Abhishek Kulkarni; A. Kaan Ata Yilmaz; Ufuk Topcu

REVIEW 3 major objections 4 minor 28 references

Dynamic Coalitions in Games on Graphs with Preferences over Temporal Goals

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper proves that, in deterministic multiplayer games on graphs with partial-order preferences over temporal goals, a leader can synthesize an admissible dynamic-coalition strategy in polynomial time, and that admissible strategies…

desk verdict The dynamic-coalition synthesis idea is plausible and worth refereeing, but Theorem 2's admissibility claim does not actually cover the full strategy space as written, and Algorithm 2 has a variable-name bug that needs cleanup. read the letter →

arxiv 2501.18022 v1 pith:YCZQKT34 submitted 2025-01-29 cs.GT

A. Kaan Ata Yilmaz , Abhishek Kulkarni , Ufuk Topcu This is my paper · ORCID

classification cs.GT

keywords dynamiccoalitionsgamesongraphspartial-orderpreferencestemporalgoalsadmissibilitymaximalsurewinningstrategysynthesispolynomial-timealgorithm

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Sequential decision-making in multi-agent systems often requires players to form temporary coalitions to reach temporal goals that no single player can force on its own. This paper studies such settings as deterministic multiplayer games on graphs, where one leader, P1, proposes a coalition and a joint action in each round, players outside the coalition are assumed to follow admissible strategies, and the subclass restricts the leader to forming a coalition with at most one other player while the rest act independently. The paper's central claim is that admissible strategies—strategies no alternative can strictly improve in the worst case over the player's least-preferred outcomes—always exist in this subclass, and that an algorithm can synthesize them in polynomial time in the size of the product game. The mechanism is a rank-based value function that lets the leader progress toward states with lower rank by cooperating with at most one partner at a time. The paper also demonstrates in a blocks-world experiment that dynamic coalitions outperform fixed coalitions and that aligned preferences do not reliably encourage cooperation.

What carries the argument

The load-bearing object is the rank function of Definition 9, an order-preserving map from the preference preorder to the natural numbers, together with the value function $Val(v) = [MaxRank_i(\pi_i)]_{i\in[N]}$ that records the best rank each player can guarantee from state $v$ without cooperation. Algorithm 2 uses these to construct level sets $V_k$ of states of rank at most $k$, then repeatedly expands a frontier $U_k$ of states from which P1 can force a visit to $V_k$ either alone or with one coalition partner. The $CandV$ and $CoalV$ maps record, respectively, the value each player would obtain under each joint coalitional action and the worst-case value over all rational coalition choices, and these maps provide the admissible actions for non-leader players. The bridge to admissibility is the theorem that a maximal sure winning strategy—one that minimizes the worst achievable rank—is admissible.

What would settle it

Run Algorithm 2 on a small game in the subclass, say two players, three states, and two scLTL goals with an explicit preference order, obtain the synthesized strategy for P1, then exhaustively enumerate all finite-memory P1 strategies against rationalizable responses of the other player and compare the least-preferred outcomes under P1's preference order; if any alternative strategy yields a strictly preferred minimal outcome, Theorem 2 is false.

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Extended reading notes

Core claim

The core claim is that admissibility in games on graphs with partial-order preferences is characterized by maximal sure winning: every maximal sure winning strategy is admissible (Proposition 1), and the rank of such a strategy is the smallest rank outcome the player can guarantee against adversarial choices of the other players. Algorithm 2 turns this characterization into a synthesis procedure for the leader: it builds level sets $V_k$ of states from which P1 can force a visit to states of rank at most $k$, either alone or through a coalition $\{1,i\}$, and it discards exactly the coalitional actions that are not rationalizable (Lemma 2). The strategy produced is admissible for P1 (Theorem 2), admissible strategies for the remaining players can be extracted from the intermediate $CandV$ and $CoalV$ maps, such a profile exists in every game of the subclass, and the procedure runs in $\mathcal{O}(r^1_{\max}|V|(|A_1|+\sum_{j=2}^{N}|A_j||A_1|))$ time. The blocks-world experiment supports the corollary that dynamic coalitions can achieve outcomes no fixed coalition can guarantee. The main text notes that the proofs of Lemma 1 and subsequent results appear in the supplementary material.

Load-bearing premise

The argument assumes that players not in the coalition reliably follow their admissible strategies and that a coalition member accepts a proposal exactly when the proposed joint action is admissible for them, even though the game's transition function does not specify what happens if a player rejects or deviates; without such a behavioral rule, the admissibility guarantee is not well defined.

Editorial extensions

If this is right

If the central claim is correct, coalition formation and control strategy synthesis can be solved together rather than separately, at least in the subclass where P1 cooperates with at most one other player per round.
The polynomial-time guarantee means the algorithm can be applied to product games of practical size without enumerating all possible coalition structures.
Dynamic coalitions can be strictly better than fixed ones: in the blocks-world example, P1 must switch partners between rounds to achieve its most preferred temporal goal, something no single fixed coalition can accomplish.
Preference alignment is not a reliable predictor of cooperation: the experiments exhibit a case where P1 cooperates with a player whose preferences conflict with its own, while aligned preferences do not always produce coalitions.
The $CandV$ and $CoalV$ structures yield admissible strategies for all players, not just the leader, so the output is an admissible strategy profile rather than a single strategy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's own examples leave open whether the coalitional actions it keeps correspond to stable coalitions in the classical core sense; one testable extension is to check whether the rationalizability filter yields coalition structures that are stable under repeated play.
Since maximal sure winning was originally defined for two-player stochastic games with preferences, the same rank-and-value construction is a plausible route to generalize dynamic-coalition synthesis to stochastic games, though the paper only mentions stochastic generalization as future work.
The counter-intuitive preference-alignment result is based on two illustrative paths in one blocks-world instance; a systematic random-game study counting coalition switches against pairwise preference distance could determine whether the pattern is structural or an artifact of the example.
The paper notes but does not prioritize social welfare, yet its second blocks-world path satisfies all players' specifications; an extension could deliberately optimize the vector of guaranteed ranks and compare welfare outcomes.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague, quick take on arXiv:2501.18022. The core idea is good: in a subclass of deterministic multiplayer games where P1 proposes a coalition and joint actions each round, and others follow admissible strategies, they give a polynomial-time algorithm that synthesizes an admissible strategy for P1, using maximal sure winning and a rank-based value function. The connection between admissibility and maximal sure winning is a reasonable extension, and the blocks-world example illustrates the benefit of dynamic over fixed coalitions. If the correctness claim holds, this is useful for multi-agent planning.

What the paper does well: it makes the model explicit enough to extend, gives a value-function characterization, proves existence of admissible profiles in the subclass, and states complexity. It also leans on prior work (Kulkarni et al. 2025, Rahmani et al. 2024) rather than hiding it, and the central algorithm is a genuine new extension, not a rehash.

Now the soft spots, in proportion. The stress-test concern is real and load-bearing. Theorem 2's proof says that by Lemma 2, no alternative strategy can enforce a state of rank at most l' because Lemma 2 only rules out sequences of rationalizable joint actions. But P1's strategy space as defined is unrestricted: any map from states to coalitions and joint actions. Nothing in Definition 1 or the acceptance rule specifies what happens when P1 proposes a non-admissible action, or when a coalition member rejects. So the 'therefore' in Theorem 2 does not go through for the full strategy space. This is not a cosmetic gap; the admissibility guarantee is undefined on the domain where it is claimed. The fix is to formalize the game semantics: either restrict P1 to rationalizable proposals and prove that restriction is without loss, or define rejection states and re-prove the theorem. That is doable, but as written the central theorem is not proven.

Also minor but real: Algorithm 2 uses k as both the iteration counter and the player index in lines 22-25; this corrupts the loop termination and the CoalV update. A rename (e.g., i for players) is needed.

There are smaller presentation issues: Assumption 1 restricts coalitions to size at most 2, which is fine but limits generality; the paper should say more about why that subclass is interesting. No code or data for the experiment, just illustrative figures—fine for a theory paper, but not reproducible.

Bottom line: the idea deserves serious refereeing and the gaps look fixable, but the version I read is not correct as a formal paper. I would send it to review with a 'major revision' expectation, and I'd want the semantics of proposal acceptance and the proof of Theorem 2 redone.

Referee Report

3 major / 4 minor

Summary. The paper studies deterministic multiplayer games on graphs where a leader (P1) dynamically proposes a coalition and joint actions each round, while non-members follow admissible strategies. The authors extend the concept of admissibility to preferences over temporal goals, define a rank-based value function, and present Algorithm 2 to synthesize an admissible strategy for P1, claiming polynomial-time complexity and existence of admissible profiles in the considered subclass. The contributions are illustrated in a BlocksWorld domain, with evidence that dynamic coalitions outperform fixed ones and that preference alignment does not straightforwardly predict coalition formation.

Significance. If the technical issues were resolved, the paper would make a useful contribution by integrating coalition formation and strategy synthesis under incomplete preferences, and by connecting maximal sure winning with admissibility in a multiplayer setting. The proposed algorithm is a concrete, potentially practical construction, and the experimental illustration raises an interesting qualitative point about cooperation under aligned preferences. However, the central admissibility guarantee currently rests on an under-specified game model and a flawed proof of Proposition 1, so the significance cannot be fully assessed until these are repaired.

major comments (3)

[Section 3, Definition 1 and Theorem 2] The game model does not define what happens when P1 proposes a joint action that is not admissible for a coalition member, or when a member rejects a proposal. The text says coalition members "must accept the proposal if the proposed joint action is admissible for them," but the transition function T and the P1 strategy space (a map from states to a coalition and a joint action) allow non-admissible proposals to be legal moves. Theorem 2's proof uses Lemma 2 to conclude that any other strategy π' has MaxRank1(π) ≤ MaxRank1(π'), but Lemma 2 only characterizes rationalizable joint actions; it says nothing about strategies that propose non-rationalizable or rejected actions. Under the natural reading that such proposals are legal, the discarded proposal may give P1 a strictly lower rank, contradicting admissibility. Under the reading that such proposals are illegal or trigger rejection, the semantics and the strategy space must be formalized. This gap is load-bearing because the admissibility claim quantifies over all P1 strategies.
[Algorithm 2, lines 4 and 22-26] The variable k is used both as the loop counter in the repeat-until loop and as the player index in "for k ∈ [N]\{1}" on line 22. After the inner loop executes, k is overwritten to the last player index (or N-1), so the loop condition "until V_{k+1} = V_k" on line 27 no longer refers to the intended level-set index. This makes the loop termination and the stated time complexity O(r1_max |V|(...)) ill-defined. The player index should be renamed (e.g., j) and the pseudocode corrected.
[Section 4.1, proof of Proposition 1] The proof of Proposition 1 misstates Definition 6. It says "for every minimal path ρ′ in Min{Paths(π′_i)}, there exists a minimal path ρ ∈ Min{Paths(π_i)} such that ρ′ ≻_i ρ," but Definition 6 states the opposite direction: for every ρ ∈ Min(π_i), there exists ρ′ ∈ Min(π′_i) such that L(ρ) ≻ L(ρ′). With the correct direction, the inequality concluded as MaxRank_i(π_i) > MaxRank_i(π′_i) does not follow; from L(ρ) ≻ L(ρ′) one gets Rank(ρ) < Rank(ρ′), which implies MaxRank_i(π′_i) > MaxRank_i(π_i), not a contradiction. Since Proposition 1 is a key ingredient of Theorem 2, this proof error must be repaired.

minor comments (4)

[Section 2.3 and Lemma 1] The notation for rank is used inconsistently: Definition 9 assigns a rank to a state u, while Lemma 1 uses Rank_i(w) for a word and the proof refers to Rank_i(ρ). Please define the rank of a path/word explicitly and use consistent notation throughout.
[Algorithm 2, lines 14-18] The expressions on lines 15-16 are under-specified: "max{CoalVi(∆(v,aC,aj)}" is missing a closing brace and does not indicate the set over which the maximum is taken (presumably over a_{-C}). Clarify the quantifiers so the definitions of c_j and a_j are unambiguous.
[Figures 2 and 3] The annotation "CoalV : [0,1]" in the figures has only two entries while the game has three players; the text should explain this notation or correct the displayed vectors.
[Section 5.1] The discussion of Figure 2 refers to "the value of S2 for P3 is 3" and "rank 1 for P3" with the notation CoalV(S3), but the relationship between Val, CoalV, and rank is not defined in the main text; please state how CoalV is derived from the algorithm's output and how it is read in the examples.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: Algorithm 2's admissibility claim is a new construction from rank and value primitives, and the same-author citations used are independent of the target result.

full rationale

The central claim, Theorem 2, is not obtained by renaming an input or by a definitional identity. The rank function (Definition 9) is an order-preserving map on product-game states derived from the preference relations; the value function (Algorithm 1) computes least guaranteed ranks; Proposition 1 is proved from Lemma 1 rather than assumed; and Lemma 2 characterizes the algorithm's pruning rule in terms of Definition 10. None of these premises is stated in terms of 'the strategy produced by Algorithm 2 is admissible', so no equation in the paper reduces to its own input. The paper's reliance on [Kulkarni et al., 2025] for maximal sure winning and for the template of Algorithm 1 is a normal extension of prior peer-reviewed work: the cited results assume two-player stochastic games without dynamic coalitions and therefore do not already contain the target theorem. A separate correctness concern exists: the proof of Theorem 2 says 'any other strategy π′ must satisfy MaxRank1(π) ≤ MaxRank1(π′)' after Lemma 2, which only discusses rationalizable joint actions, and the transition function in Definition 1 leaves rejected or non-rationalizable proposals undefined. This is a genuine gap in the proof as printed, but it is a missing quantifier argument, not a circular reduction; the conclusion is not embedded in the premises by construction.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No numeric free parameters are fitted; the central claim rests on standard order theory, the cited prior algorithm for maximal sure winning, the leader-centric subclass restriction, and an informally specified acceptance rule for coalition proposals.

assumptions (4)

standard math Every preorder on a countable set has non-empty maximal elements (used in rank decomposition, Def. 9).
Needed to ensure ranks are well-defined for all states; standard order theory.
domain assumption The product game H and rank computation from Kulkarni et al. 2025 correctly compute maximal sure winning strategies.
Algorithm 1 is adapted from the authors' prior work and soundness is cited rather than fully re-proved.
domain assumption Assumption 1: every coalition structure contains only singleton coalitions or exactly one pair {1,i}.
Restricts the game class to leader-plus-one-partner; the algorithm and its proof rely on this limitation.
domain assumption Coalition members accept P1's proposal iff the proposed joint action is admissible; non-coalition players follow admissible strategies.
Stated informally in Section 3 but not formalized in the transition function; required for Theorem 2's proof.

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Cite this review

Pith. "Pith review of Dynamic Coalitions in Games on Graphs with Preferences over Temporal Goals." pith.science (2026). https://pith.science/paper/YCZQKT34

@misc{pith2026250118022,
  author       = {Pith},
  title        = {Pith review of: Dynamic Coalitions in Games on Graphs with Preferences over Temporal Goals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YCZQKT34}},
  note         = {Machine review of arXiv:2501.18022}
}

read the original abstract

In multiplayer games with sequential decision-making, self-interested players form dynamic coalitions to achieve most-preferred temporal goals beyond their individual capabilities. We introduce a novel procedure to synthesize strategies that jointly determine which coalitions should form and the actions coalition members should choose to satisfy their preferences in a subclass of deterministic multiplayer games on graphs. In these games, a leader decides the coalition during each round and the players not in the coalition follow their admissible strategies. Our contributions are threefold. First, we extend the concept of admissibility to games on graphs with preferences and characterize it using maximal sure winning, a concept originally defined for adversarial two-player games with preferences. Second, we define a value function that assigns a vector to each state, identifying which player has a maximal sure winning strategy for certain subset of objectives. Finally, we present a polynomial-time algorithm to synthesize admissible strategies for all players based on this value function and prove their existence in all games within the chosen subclass. We illustrate the benefits of dynamic coalitions over fixed ones in a blocks-world domain. Interestingly, our experiment reveals that aligned preferences do not always encourage cooperation, while conflicting preferences do not always lead to adversarial behavior.

Figures

Figures reproduced from arXiv: 2501.18022 by the authors.

**Figure 2.** The first dynamic coalition formation strategy tha [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** The second dynamic coalition formation strategy t [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

[1]

Henzinger, and Orna Kupferman

[Alur et al., 2002] Rajeev Alur, Thomas A. Henzinger, and Orna Kupferman. Alternating-time temporal logic. J. ACM, 49(5):672–713, September

work page 2002
[3]

Nash equilibrium in games with incomplete preferences

[Bade, 2005] Sophie Bade. Nash equilibrium in games with incomplete preferences. Economic Theory , 26:309–332,

work page 2005
[10]

Automata logics, and inﬁnite games: a guide to current research

[Gr¨ adelet al., 2002] Erich Gr¨ adel, Wolfgang Thomas, and Thomas Wilke, editors. Automata logics, and inﬁnite games: a guide to current research . Springer-V erlag, Berlin, Heidelberg,

work page 2002
[11]

[Guelev, 2020] Dimitar P . Guelev. Reasoning about tem- porary coalitions and ltl-deﬁnable ordered objectives in inﬁnite concurrent multiplayer games. CoRR, abs/2011.03724,

work page Pith review arXiv 2020
[17]

Kulkarni, Jie Fu, and Ufuk Topcu

[Kulkarni et al., 2025] Abhishek N. Kulkarni, Jie Fu, and Ufuk Topcu. Sequential decision making in stochastic games with incomplete preferences over temporal objec- tives. In Proceedings of the AAAI Conference on Artiﬁcial Intelligence,

work page 2025
[21]

Lifting preferences over alternatives to preferences over sets of alternatives: The complexity of recognizing desirable families of sets

[Maly, 2020] Jan Maly. Lifting preferences over alternatives to preferences over sets of alternatives: The complexity of recognizing desirable families of sets. In Proceedings of the AAAI Conference on Artiﬁcial Intelligence , volume 34, pages 2152–2159,

work page 2020
[22]

Principles of artiﬁcial intel- ligence

[Nilsson, 2014] Nils J Nilsson. Principles of artiﬁcial intel- ligence. Morgan Kaufmann,

work page 2014
[26]

Maximization and the act of choice

[Sen, 1997] Amartya Sen. Maximization and the act of choice. Econometrica: Journal of the Econometric So- ciety, pages 745–779,

work page 1997

Show all 28 references

[28]

Coalition F ormation between Self-Interested Heterogeneous Actors

[van Wissen, 2009] Arlette van Wissen. Coalition F ormation between Self-Interested Heterogeneous Actors . Citeseer,

2009
[1984]

Nash equilibria in concurrent games with b¨ uchi objectives

[Bouyer et al., 2011] Patricia Bouyer, Romain Brenguier, Nicolas Markey, and Michael Ummels. Nash equilibria in concurrent games with b¨ uchi objectives. InIARCS Annual Conference on F oundations of Software T echnology and Theoretical Computer Science (FSTTCS

2011
[1994]

Probabilistic planning with partially or- dered preferences over temporal goals

[Rahmani et al., 2023] Hazhar Rahmani, Abhishek N Kulka- rni, and Jie Fu. Probabilistic planning with partially or- dered preferences over temporal goals. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 5702–5708. IEEE,

2023
[1997]

The trolley prob- lem

[Thomson, 1984] Judith Jarvis Thomson. The trolley prob- lem. Y ale LJ, 94:1395,

1984
[2001]

[Kupferman et al., 2016] Orna Kupferman, Giuseppe Perelli, and Moshe Y . V ardi. Synthesis with rational environments. Ann. Math. Artif. Intell. , 78(1):3–20,

2016
[2002]

Dynamic coalition formation and the core

[Arnold and Schwalbe, 2002 ] Tone Arnold and Ulrich Schwalbe. Dynamic coalition formation and the core. Journal of Economic Behavior & Organization , 49(3):363–380,

2002
[2003]

Kulkarni, Jie Fu, and Ufuk Topcu

[Kulkarni et al., 2024] Abhishek N. Kulkarni, Jie Fu, and Ufuk Topcu. Nash equilibrium in games on graphs with incomplete preferences,

2024
[2005]

Extending an order on a set to the power set: Some remarks on kannai and peleg’s approach

[Barber´ a and Pattanaik, 1984] Salvador Barber´ a and Pras- anta K Pattanaik. Extending an order on a set to the power set: Some remarks on kannai and peleg’s approach. Jour- nal of Economic Theory , 32(1):185–191,

1984
[2006]

Preferences

[Hansson and Gr¨ une-Y anoff, 2024] Sven Ove Hansson and Till Gr¨ une-Y anoff. Preferences. In Edward N. Zalta and Uri Nodelman, editors, The Stanford Encyclopedia of Phi- losophy. Metaphysics Research Lab, Stanford University, Winter 2024 edition,

2024
[2008]

Assume-admissible synthesis

[Brenguier et al., 2015] Romain Brenguier, Jean-Franc ¸ois Raskin, and Ocan Sankur. Assume-admissible synthesis. CoRR, abs/1507.00623,

2015 arXiv
[2010]

[Davey, 2002] BA Davey

Special Is- sue: 18th International Conference on Concurrency The- ory (CONCUR 2007). [Davey, 2002] BA Davey. Introduction to Lattices and Or- der. Cambridge University Press,

2007
[2011]

Admissibility in games

[Brandenburger et al., 2008] Adam Brandenburger, Amanda Friedenberg, and H Jerome Keisler. Admissibility in games

2008
[2014]

A course in game theory

[Osborne, 1994] Martin J Osborne. A course in game theory. MIT Press,

1994
[2015]

Henzinger, and Nir Piterman

[Chatterjee et al., 2010] Krishnendu Chatterjee, Thomas A. Henzinger, and Nir Piterman. Strategy logic. Informa- tion and Computation , 208(6):677–693,

2010
[2016]

Multiplayer stackelberg–nash game for nonlinear system via value iteration-based integral rein- forcement learning

[Li et al., 2020] Man Li, Jiahu Qin, Nikolaos M Freris, and Daniel WC Ho. Multiplayer stackelberg–nash game for nonlinear system via value iteration-based integral rein- forcement learning. IEEE Transactions on Neural Net- works and Learning Systems , 33(4):1429–1440,

2020
[2020]

Coalition formation games: A survey, dec

[Hajdukov´ a, 2006] Jana Hajdukov´ a. Coalition formation games: A survey, dec

2006
[2022]

Coalition formation as a dynamic process

[Konishi and Ray, 2003] Hideo Konishi and Debraj Ray. Coalition formation as a dynamic process. Journal of Eco- nomic Theory, 110(1):1–41,

2003
[2023]

Preference-based planning in stochastic environments: From partially-ordered temporal goals to most preferred policies

[Rahmani et al., 2024] Hazhar Rahmani, Abhishek N Kulka- rni, and Jie Fu. Preference-based planning in stochastic environments: From partially-ordered temporal goals to most preferred policies. arXiv preprint arXiv:2403.18212,

2024 arXiv
[2024]

Coalitional strategic games

[Hara, 2022] Kazuhiro Hara. Coalitional strategic games. Journal of Economic Theory , 204:105512, 9

2022
[2025]

Model checking of safety proper- ties

[Kupferman and V ardi, 2001] Orna Kupferman and Moshe Y V ardi. Model checking of safety proper- ties. F ormal methods in system design , 19:291–314,

2001

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Henzinger, and Orna Kupferman

[Alur et al., 2002] Rajeev Alur, Thomas A. Henzinger, and Orna Kupferman. Alternating-time temporal logic. J. ACM, 49(5):672–713, September

work page 2002

[2] [3]

Nash equilibrium in games with incomplete preferences

[Bade, 2005] Sophie Bade. Nash equilibrium in games with incomplete preferences. Economic Theory , 26:309–332,

work page 2005

[3] [10]

Automata logics, and inﬁnite games: a guide to current research

[Gr¨ adelet al., 2002] Erich Gr¨ adel, Wolfgang Thomas, and Thomas Wilke, editors. Automata logics, and inﬁnite games: a guide to current research . Springer-V erlag, Berlin, Heidelberg,

work page 2002

[4] [11]

[Guelev, 2020] Dimitar P . Guelev. Reasoning about tem- porary coalitions and ltl-deﬁnable ordered objectives in inﬁnite concurrent multiplayer games. CoRR, abs/2011.03724,

work page Pith review arXiv 2020

[5] [17]

Kulkarni, Jie Fu, and Ufuk Topcu

[Kulkarni et al., 2025] Abhishek N. Kulkarni, Jie Fu, and Ufuk Topcu. Sequential decision making in stochastic games with incomplete preferences over temporal objec- tives. In Proceedings of the AAAI Conference on Artiﬁcial Intelligence,

work page 2025

[6] [21]

Lifting preferences over alternatives to preferences over sets of alternatives: The complexity of recognizing desirable families of sets

[Maly, 2020] Jan Maly. Lifting preferences over alternatives to preferences over sets of alternatives: The complexity of recognizing desirable families of sets. In Proceedings of the AAAI Conference on Artiﬁcial Intelligence , volume 34, pages 2152–2159,

work page 2020

[7] [22]

Principles of artiﬁcial intel- ligence

[Nilsson, 2014] Nils J Nilsson. Principles of artiﬁcial intel- ligence. Morgan Kaufmann,

work page 2014

[8] [26]

Maximization and the act of choice

[Sen, 1997] Amartya Sen. Maximization and the act of choice. Econometrica: Journal of the Econometric So- ciety, pages 745–779,

work page 1997