The Mathematics of Coordinated Inference

Hardin, Christopher S.; Taylor, Alan D.

doi:10.1007/978-3-319-01333-6

Cited by 12 publications

(18 citation statements)

References 0 publications

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“…In the case of

K = {0, 1}

, a predictor which satisfies the first clause in the above definition is called a signaling predictor [3, Theorem 3.3.2]. It is obvious that, when

K = {double-struckZ}_{2}

, a signal‐biased predictor is a signaling predictor.…”

Section: Resultsmentioning

confidence: 99%

“…The famous mathematical puzzles known as puzzles of prisoners and hats or hat guessing games are originally suggested by Gardner [1], and have been studied in connection with combinatorics and set theory. Set‐theoretic studies before 2013 of hat puzzles are summarized by Hardin and Taylor [3].…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we adopt the formalization of hat puzzles in the Hardin–Tayler book [3]. We call the players agents instead of “prisoners” and the set of agents is often denoted by A .…”

Section: Introductionmentioning

confidence: 99%

“…Using the axiom of choice, in the case of

| K | = 2

, Lenstra proved a significant result (cf. [3, Theorem 3.3.1] for a proof). Theorem Consider a hat puzzle with an arbitrary set A of agents, the set

K = {0, 1}

of colors, complete visibility and simultaneous declaration.…”

Section: Introductionmentioning

confidence: 99%

“…Hardin and Taylor showed, in

ZF + DC

, that there is a signaling predictor if and only if there is a Lenstra predictor (cf. [3, Theorem 3.3.2]). Theorem With an arbitrary set A of agents and the set

K = {0, 1}

of hat colors, the following conditions are equivalent: (1)The visibility graph V is complete, and in the puzzle of one‐in‐advance protocol, there is a predictor under which all agents but the signaler guess correctly. (2)In the puzzle of simultaneous declaration, there is a predictor under which all agents guess correctly or all agents guess incorrectly. …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Strategic equivalence among hat puzzles of various protocols with many colors

Kada

Shizuma

2020

Mathematical Logic Qtrly

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“…In the case of

K = {0, 1}

, a predictor which satisfies the first clause in the above definition is called a signaling predictor [3, Theorem 3.3.2]. It is obvious that, when

K = {double-struckZ}_{2}

, a signal‐biased predictor is a signaling predictor.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Using the axiom of choice, in the case of

| K | = 2

, Lenstra proved a significant result (cf. [3, Theorem 3.3.1] for a proof). Theorem Consider a hat puzzle with an arbitrary set A of agents, the set

K = {0, 1}

of colors, complete visibility and simultaneous declaration.…”

Section: Introductionmentioning

confidence: 99%

“…Hardin and Taylor showed, in

ZF + DC

, that there is a signaling predictor if and only if there is a Lenstra predictor (cf. [3, Theorem 3.3.2]). Theorem With an arbitrary set A of agents and the set