Were there no Corona virus pandemic, German Universities would regularly start the summer semester in around a month (soon after Eastern). Now, it seems likely that courses will be offered digitally and students must learn from home. If you have a cou... [Read more...]

Based on Robert S. Mueller’s investigations about foreign involvement in the 2016 US presidential elections US Congress created this website with the title “Exposing Russia’s Effort to Sow Discord Online: The Internet Research Agency and Advertis... [Read more...]

This post continues my first post on game theoretic analysis with the package RelationalContacts in R. Here we look at more complex infinite horizon games with endogenous states. I also illustrate how one can explicitly combine relational contracting and hold-up concerns. The following code specifies a game with 3 states:

<span class="n">library</span><span class="p">(</span><span class="n">RelationalContracts</span><span class="p">)</span><span class="w">
</span><span class="n">g</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rel_game</span><span class="p">(</span><span class="s2">"Mutual Gift Game with Endogenous Vulnerability"</span><span class="p">)</span><span class="w"> </span><span class="o">%>%</span><span class="w">
  </span><span class="n">rel_param</span><span class="p">(</span><span class="n">vul</span><span class="o">=</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">delta</span><span class="o">=</span><span class="m">0.3</span><span class="p">)</span><span class="w"> </span><span class="o">%>%</span><span class="w">
  </span><span class="n">rel_state</span><span class="p">(</span><span class="s2">"x_0"</span><span class="p">,</span><span class="w">
    </span><span class="n">A1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">list</span><span class="p">(</span><span class="n">move</span><span class="o">=</span><span class="nf">c</span><span class="p">(</span><span class="s2">"vul"</span><span class="p">,</span><span class="s2">"not"</span><span class="p">)),</span><span class="w">
    </span><span class="n">pi1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w">
    </span><span class="n">pi2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w">
  </span><span class="p">)</span><span class="w"> </span><span class="o">%>%</span><span class="w">
  </span><span class="n">rel_transition</span><span class="p">(</span><span class="s2">"x_0"</span><span class="p">,</span><span class="s2">"x_not"</span><span class="p">,</span><span class="n">move</span><span class="o">=</span><span class="s2">"not"</span><span class="p">,</span><span class="n">prob</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%>%</span><span class="w">
  </span><span class="n">rel_transition</span><span class="p">(</span><span class="s2">"x_0"</span><span class="p">,</span><span class="s2">"x_vul"</span><span class="p">,</span><span class="n">move</span><span class="o">=</span><span class="s2">"vul"</span><span class="p">,</span><span class="n">prob</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%>%</span><span class="w">
  </span><span class="n">rel_state</span><span class="p">(</span><span class="s2">"x_not"</span><span class="p">,</span><span class="w">
    </span><span class="n">A1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">list</span><span class="p">(</span><span class="n">e1</span><span class="o">=</span><span class="n">seq</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="m">1</span><span class="p">,</span><span class="n">by</span><span class="o">=</span><span class="m">0.1</span><span class="p">)),</span><span class="w">
    </span><span class="n">A2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">list</span><span class="p">(</span><span class="n">e2</span><span class="o">=</span><span class="n">seq</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="m">1</span><span class="p">,</span><span class="n">by</span><span class="o">=</span><span class="m">0.1</span><span class="p">)),</span><span class="w">
    </span><span class="n">pi1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">~</span><span class="w"> </span><span class="n">e2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">0.5</span><span class="o">*</span><span class="n">e1</span><span class="o">^</span><span class="m">2</span><span class="p">,</span><span class="w">
    </span><span class="n">pi2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">~</span><span class="w"> </span><span class="n">e1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">0.5</span><span class="o">*</span><span class="n">e2</span><span class="o">^</span><span class="m">2</span><span class="w">
  </span><span class="p">)</span><span class="w"> </span><span class="o">%>%</span><span class="w">
  </span><span class="n">rel_state</span><span class="p">(</span><span class="s2">"x_vul"</span><span class="p">,</span><span class="w">
    </span><span class="n">A1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">list</span><span class="p">(</span><span class="n">e1</span><span class="o">=</span><span class="n">seq</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="m">1</span><span class="p">,</span><span class="n">by</span><span class="o">=</span><span class="m">0.1</span><span class="p">)),</span><span class="w">
    </span><span class="n">A2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">list</span><span class="p">(</span><span class="n">e2</span><span class="o">=~</span><span class="nf">c</span><span class="p">(</span><span class="o">-</span><span class="n">vul</span><span class="p">,</span><span class="n">seq</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="m">1</span><span class="p">,</span><span class="n">by</span><span class="o">=</span><span class="m">0.1</span><span class="p">))),</span><span class="w">
    </span><span class="n">pi1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">~</span><span class="w"> </span><span class="n">e2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">0.5</span><span class="o">*</span><span class="n">e1</span><span class="o">^</span><span class="m">2</span><span class="p">,</span><span class="w">
    </span><span class="n">pi2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">~</span><span class="w"> </span><span class="n">e1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">0.5</span><span class="o">*</span><span class="n">pmax</span><span class="p">(</span><span class="n">e2</span><span class="p">,</span><span class="m">0</span><span class="p">)</span><span class="o">^</span><span class="m">2</span><span class="w">
  </span><span class="p">)</span><span class="w">
</span>

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