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arxiv: 1907.06862 · v1 · pith:QFHLYVAFnew · submitted 2019-07-16 · 💻 cs.GT · cs.MA

The Impact of Tribalism on Social Welfare

Seunghee Han , Matvey Soloviev , Yuwen Wang This is my paper

Pith reviewed 2026-05-24 20:49 UTC · model grok-4.3

classification 💻 cs.GT cs.MA
keywords tribalismprice of anarchystrategic gamesaltruismcongestion gamesnetwork contribution gamesequilibrium analysis
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The pith

Tribal altruism within player subgroups can produce worse equilibrium social welfare than either pure selfishness or full altruism.

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

The paper defines a τ-tribal extension of any strategic game in which players belonging to the same tribe update their subjective cost functions to reflect mutual altruism. It introduces the Price of Tribalism as the ratio between social welfare at the worst equilibrium of this extension and the optimal social welfare. In friendship-clique games, network contribution games, and atomic linear congestion games, this ratio exceeds the Price of Anarchy both for purely selfish players and for fully altruistic players, with the elevation holding under several equilibrium concepts and with matching upper bounds supplied for each class. A reader would care because the finding indicates that intermediate forms of group loyalty can degrade collective outcomes more than either extreme.

Core claim

In the τ-tribal extension of friendship-clique games, network contribution games, and atomic linear congestion games, the Price of Tribalism exceeds the Price of Anarchy of the original game under selfish play and also exceeds the Price of Anarchy under fully altruistic play. The comparison holds for a range of equilibrium notions, and the paper supplies matching upper bounds on the Price of Tribalism in each setting.

What carries the argument

The τ-tribal extension of a strategic game, which revises only each player's subjective cost function to encode intra-tribe altruism while the objective social-welfare function remains unchanged; the Price of Tribalism is the welfare ratio it induces at worst equilibrium versus optimum.

If this is right

  • Friendship-clique games exhibit a Price of Tribalism strictly larger than both the selfish and the altruistic Price of Anarchy.
  • Network contribution games likewise show an elevated Price of Tribalism relative to the two baseline notions.
  • Atomic linear congestion games display the same ordering, with the tribal price exceeding both the selfish and the altruistic prices.
  • Matching upper bounds exist for the Price of Tribalism in each of the three game classes.
  • The elevation appears under multiple equilibrium concepts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the modeling choice holds, interventions that weaken tribe boundaries could improve equilibrium welfare in these games without requiring full altruism.
  • The same extension technique could be applied to other strategic settings in which identity partitions affect perceived payoffs.
  • Empirical measurement of intra-group cost weighting in real congestion or contribution settings would test whether the predicted ordering appears outside the modeled examples.

Load-bearing premise

Mutual altruism inside tribes is fully captured by changing only the subjective costs that players use when choosing strategies, without altering the objective social-welfare function.

What would settle it

An explicit equilibrium computation, in any one of the three game families, in which the worst-case social welfare under the τ-tribal extension is no lower than the worst-case welfare under either selfish or fully altruistic play.

Figures

Figures reproduced from arXiv: 1907.06862 by Matvey Soloviev, Seunghee Han, Yuwen Wang.

Figure 1
Figure 1. Figure 1: Le : An OPT/2 selfish equilibrium. Right: An OPT/3 tribal equilibrium. congestion games with social context given by a general graph, which in our setting (i.e. when the graph is a collection of disjoint cliques) have a matching lower and upper bound of 4. Due to the generality of the social context model, we consider our model to be of independent interest. 4 EXAMPLES 4.1 Social grouping games A simple fo… view at source ↗
read the original abstract

We explore the impact of mutual altruism among the players belonging to the same set -- their tribe -- in a partition of all players in arbitrary strategic games upon the quality of equilibria attained. To this end, we introduce the notion of a {\tau}-tribal extension of an arbitrary strategic game, in which players' subjective cost functions are updated to reflect this, and the associated Price of Tribalism, which is the ratio of the social welfare of the worst Nash equilibrium of the tribal extension to that of the optimum of social welfare. We show that in a well-known game of friendship cliques, network contribution games as well as atomic linear congestion games, the Price of Tribalism is higher than the Price of Anarchy of either the purely selfish players or fully altruistic players (i.e. ones who seek to maximise the social welfare). This phenomenon is observed under a variety of equilibrium concepts. In each instance, we present upper bounds on the Price of Tribalism that match the lower bounds established by our example.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper introduces the τ-tribal extension of an arbitrary strategic game, in which each player's subjective cost is a convex combination of its own cost and the costs of its tribe-mates (with parameter τ), while the objective social-welfare function remains the sum of the original individual costs. It defines the Price of Tribalism (PoT) as the ratio of the social welfare of the worst Nash equilibrium (or other equilibrium concept) of the tribal extension to the optimal social welfare. The central claim is that, in friendship-clique games, network contribution games, and atomic linear congestion games, this PoT strictly exceeds the Price of Anarchy of both the purely selfish game and the fully altruistic game; matching upper and lower bounds are provided for each class.

Significance. If the results hold under the stated modeling choices, the work shows that intermediate, group-restricted altruism can produce strictly worse equilibrium welfare than either pure selfishness or global altruism. This is a non-obvious comparative-static result across three standard game families and multiple equilibrium notions, with tight bounds. The explicit construction of examples that achieve the bounds and the provision of matching analytic upper bounds are concrete strengths.

major comments (1)
  1. [Definition of the τ-tribal extension] Definition of the τ-tribal extension (abstract and §2): the central claim that PoT exceeds both the selfish and fully-altruistic PoA rests on keeping the objective social-welfare function equal to the sum of the original individual costs while only the subjective costs incorporate tribal altruism. If the objective welfare were instead redefined to include the same convex-combination terms that appear in the players' utilities, both the social optimum and the set of equilibria would shift, and the claimed strict inequality could fail to hold. The manuscript must either justify why the objective welfare is left unchanged or examine the alternative definition.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for highlighting the modeling choice in the definition of the τ-tribal extension. We address the concern directly below and will revise the manuscript to include an explicit justification.

read point-by-point responses

  1. Referee: Definition of the τ-tribal extension (abstract and §2): the central claim that PoT exceeds both the selfish and fully-altruistic PoA rests on keeping the objective social-welfare function equal to the sum of the original individual costs while only the subjective costs incorporate tribal altruism. If the objective welfare were instead redefined to include the same convex-combination terms that appear in the players' utilities, both the social optimum and the set of equilibria would shift, and the claimed strict inequality could fail to hold. The manuscript must either justify why the objective welfare is left unchanged or examine the alternative definition.

    Authors: The objective social welfare is deliberately kept as the sum of the original individual costs because it captures the true, external societal cost independent of players' internal perceptions. The τ-tribal model modifies only subjective costs to reflect altruism toward tribe members, which affects equilibrium selection but leaves the actual welfare metric unchanged. This separation follows standard practice in the altruism-in-games literature, where social optima are evaluated on true costs while equilibria reflect perceived utilities. Redefining objective welfare to incorporate the same convex combinations would instead model a setting in which societal value itself is subjectively weighted by tribal ties—an interesting but distinct question outside the paper's scope. We will add a clarifying paragraph in §2 explaining this distinction and why the alternative definition is not adopted. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces the τ-tribal extension (subjective costs updated via convex combination within tribes) and defines Price of Tribalism as the ratio of worst NE welfare in the extension to the optimum under the fixed objective social welfare function. It then proves, via equilibrium existence, explicit examples, and matching upper/lower bounds, that this ratio exceeds both the selfish PoA and the fully-altruistic PoA in friendship cliques, network contribution games, and atomic linear congestion games. No step reduces the claimed inequality to a fitted parameter, self-referential definition, or self-citation chain; the separation between subjective utilities and objective welfare is an explicit modeling choice that enables the comparison rather than forcing the result by construction. The derivation chain is self-contained against the stated assumptions and game-specific analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the newly introduced definition of the tribal extension and on standard game-theoretic assumptions about equilibrium existence; no free parameters or invented physical entities are visible in the abstract.

axioms (1)
  • standard math Strategic games admit Nash equilibria under the modified subjective costs of the tribal extension.
    Implicit when the paper discusses Nash equilibria of the tribal extension.
invented entities (1)
  • τ-tribal extension no independent evidence
    purpose: Model mutual altruism within tribes by adjusting subjective cost functions.
    Newly defined modeling device; no independent evidence supplied in abstract.

pith-pipeline@v0.9.0 · 5703 in / 1204 out tokens · 27422 ms · 2026-05-24T20:49:11.632775+00:00 · methodology

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Reference graph

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