Algorithmic Game Theory Assignment 1

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Questions and Answers

Which literary movement is best represented by Sławomir Mrożek's "Tango"?

  • Realism
  • Theater of the Absurd (correct)
  • Existentialism
  • Romanticism

What sociopolitical context influenced the banning of Sławomir Mrożek's "Tango" in communist Poland during the 1960s and 70s?

  • Its overt celebration of traditional family values.
  • Its perceived support for capitalist ideologies.
  • Its themes of social decay and critique of authority. (correct)
  • Its endorsement of avant-garde artistic movements.

How does Jacek Dukaj's "Katedra" blend science fiction elements with other literary genres?

  • By focusing solely on technological advancements without exploring human emotions.
  • By depicting advanced technologies as inherently dystopian and dehumanizing.
  • By using futuristic settings to explore timeless philosophical and religious themes. (correct)
  • By rejecting traditional storytelling structures in favor of abstract narratives.

Which of the following best describes Artur's motivation in attempting to restore order in Sławomir Mrożek's "Tango"?

<p>A genuine desire to revitalize traditional values and familial harmony. (C)</p>
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In what way does Halina Poświatowska's poetry engage with the motifs of Eros and Thanatos?

<p>By exploring the intertwined relationship between love, desire, and mortality. (B)</p>
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How might Wislawa Szymborska's poetry be considered philosophical?

<p>It explores fundamental questions about human existence and meaning. (C)</p>
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What is the effect of irony created within Wislawa Szymborska's chosen poems?

<p>To provoke reflection on the complexities and contradictions of life. (D)</p>
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How did Marek Nowakowski depict the realities of martial law in Poland in his collection "Report on the State of War"?

<p>Through gritty, realistic depictions of everyday life under oppression. (C)</p>
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Which characteristic is NOT typically associated with grotesqueness in literature, as exemplified in Sławomir Mrożek's "Tango"?

<p>Subtle and nuanced representations of everyday life. (D)</p>
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In Jacek Dukaj's "Katedra", which human aspirations and values are suggested to be timeless?

<p>Faith, sacrifice, and artistic expression. (B)</p>
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What role does biography play in Halina Poświatowska's selected poems?

<p>It is transformed into a literary element, shaping the poems' themes and perspectives. (C)</p>
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How might the relationship between humans and artificial intelligence be explored in Jacek Dukaj's "Katedra"?

<p>Through an exploration of the boundaries between consciousness, creation, and faith. (A)</p>
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In Marek Nowakowski's "Report on the State of War", which aspect of life during martial law is LEAST likely to be portrayed?

<p>The moments of joy and celebration within the community. (D)</p>
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In "Tango", how does Sławomir Mrożek use the appearance and attire of characters in Act I to convey information about them?

<p>To satirize societal norms and class distinctions through exaggerated and absurd costumes. (B)</p>
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Compared to other literary movements, what element is most vital to the Theatre of the Absurd, of which "Tango" is an example?

<p>The abandonment of coherence and the embrace of nonsensical acts. (B)</p>
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Which of the following best describes the problems Wislawa Szymborska explores in her poetry?

<p>They touch on broad universal topics using specific language. (D)</p>
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Which of the following is NOT a function of irony in Szymborska's poetry?

<p>Offering simple solutions to life's complex problems. (A)</p>
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What is the main topic presented in the third question of section V (5)?

<p>Discussion of the relationship between people and artificial intelligence in &quot;Katedra&quot;. (C)</p>
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What is the key literary device present in the play, "Tango", which helps create a situation characterized by a mix of comedy and seriousness?

<p>Grotesque (B)</p>
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Flashcards

Teatr Absurdu

A current characterized by absurdity.

Irony

A literary method employing humor and mockery.

Science Fiction

Literary works blending scientific elements with fiction.

Grotesque

Grotesque involves exaggerated or distorted features.

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Eros and Thanatos

Love (Eros) and death (Thanatos) motifs.

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Study Notes

  • The assignment involves problems in Algorithmic Game Theory.
  • It is an individual assignment worth 5% of the final grade.
  • Submissions are due September 26 at 23:59 via Brightspace as a single PDF.
  • Solutions should be typeset and explained clearly, formally, and precisely.
  • Discussion is allowed, but solutions must be written independently.

Question 1: Second-Price Auction

  • There are two people and a single item for sale.
  • Person 1 values the item at $v_1 = 100$ and Person 2 values the item at $v_2 = 150$

Part (a)

  • Determining dominant bids for Person 1 and Person 2.

Part (b)

  • Calculating social welfare if Person 1 wins.

Part (c)

  • Calculating social welfare if Person 2 wins.

Part (d)

  • Determining if the person with the highest value always wins a second-price auction.

Question 2: Game in Normal Form with Strictly Dominant Strategies

  • Determining strictly dominant strategies for Player 1.
  • Determining strictly dominant strategies for Player 2.
  • Finding which strategies survive iterated removal of strictly dominated strategies (IRSDS).

Question 3: Nash Equilibria in Mixed Strategies

  • Finding the Nash equilibria in mixed strategies for the provided game.

Question 4: Nash Equilibria in Mixed Strategies

  • Finding the Nash equilibria in mixed strategies for the provided game.

Question 5: Existence of Nash Equilibrium in Warehouse Placement Game

  • A graph $G = (V, E)$ is given where $V$ are cities and $E$ are roads.
  • $k$ companies want to build a warehouse in a city.
  • Each company $i$ has a set $S_i \subseteq V$ where they can build.
  • Companies minimize distance to other companies' warehouses.
  • Company i's strategy: pick city $v_i \in S_i$.
  • Strategy profile: $s = (v_1, \dots, v_k)$.
  • Utility: $u_i(s) = - \min_{j \neq i} d(v_i, v_j)$, where $d(v_i, v_j)$ is the shortest path between $v_i$ and $v_j$.
  • Requires a proof that a Nash equilibrium always exists.
  • The answer should be limited to one page.

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