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TI 2004-095/1 Tinbergen Institute Discussion Paper Harsanyi Power Solutions for Graph- restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam, and Tinbergen Institute.

Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 1: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

TI 2004-095/1 Tinbergen Institute Discussion Paper

Harsanyi Power Solutions for Graph-restricted Games

René van den Brink Gerard van der Laan Vitaly Pruzhansky

Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam, and Tinbergen Institute.

Page 2: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

Tinbergen Institute The Tinbergen Institute is the institute for economic research of the Erasmus Universiteit Rotterdam, Universiteit van Amsterdam, and Vrije Universiteit Amsterdam. Tinbergen Institute Amsterdam Roetersstraat 31 1018 WB Amsterdam The Netherlands Tel.: +31(0)20 551 3500 Fax: +31(0)20 551 3555 Tinbergen Institute Rotterdam Burg. Oudlaan 50 3062 PA Amsterdam The Netherlands Tel.: +31(0)10 408 8900 Fax: +31(0)10 408 9031 Please send questions and/or remarks of non-scientific nature to [email protected]. Most TI discussion papers can be downloaded at http://www.tinbergen.nl.

Page 3: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 4: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 5: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 6: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 7: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 8: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 9: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 10: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 11: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 17: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 18: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 21: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 22: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 23: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 25: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 27: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

@tt�}?4i?| }@4i EQ> y� �? , @4T*i D�� @?_ �t }��i? M)yOEV� '

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i �ht| UL?t�_ih @ t�|�@|�L? |�@| |�ihi �t L?*) L?i t�?}*i M@?! �@��?} @? �A��5TiU��U@**)c *i| |�i M@?!t ?L| �@��?} @? �A� Mi �?_i i_ M) l ' 2> ===> q @?_ *i| T*@)ih �Mi |�i L?*) M@?! |�@| �@t @? �A�� A�i ?�4Mih Lu ��t�|t Lu U�t|L4iht Lu M@?! l 9' � |L|�i �A� Lu M@?! � �t }��i? M) $l� i @tt�4i |�@| i@U� ��t�| )�i*_t @ ULt| t@��?} Lu L?i�5Lc UL@*�|�L? V ' i�> lj U@? hi@*�3i |�i ?L?�?i}@|��i �Lh|� $lc l ' 2> = = = > q @?_ |��t |�iU�@h@U|ih�t|�U u�?U|�L? Lu |�i }@4i �t }��i? M)y EV� ' ;?=

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ULLTih@|�L? Mi|�ii? M@?! lc l 9' �c @?_ �A� M@?! � �t i^�@**) _�t|h�M�|i_ Mi|�ii? l @?_�� W? i@U� tL*�|�L? |�i T@)Lg |L |�i �A� M@?! � �t i^�@* |L Sql'2 �2$l @?_ |�i T@)Lg |LM@?! l �t �2$lc l ' 2> = = = > q�wi| �t ?L� UL?t�_ih |�i U@ti |�@| |�ihi @hi 4�*|�T*i M@?!t �@��?} @? �A�� it�TTLti |�@| |�ihi �t L?*) L?i t�?}*i M@?! ��|�L�| @? �A�� wi| i�> ===> q � �j Mi |�iti| Lu M@?!t ��L TLttitt �A�t @?_ *i| M@?! q Mi |�i M@?! ��|�L�| �A�� A�i �@*�i Lu@?) UL@*�|�L? UL?|@�?�?} M@?! q @?_ @| *i@t| L?i L|�ih M@?! i^�@*t |�i |L|@* ?�4Mih LuU�t|L4iht $q Lu M@?! q� 5Lc |�i U�@h@U|ih�t|�U u�?U|�L? �t }��i? M)y EV� ' + $q> �u q 5 V @?_ mVm � 2>f> L|�ih��ti�W| uL**L�t |�@| |�i _���_i?_t @hi }��i? M){VEy� '

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5�?Ui y ' yOc |�i �)ihtL? �@*�i i^�@*t |�i 5�@T*i) �@*�iG �EQ> y> O� ' #EQ> y�� `�i?q � �c |�i ULhi Lu |�i }@4i UL?t�t|t Lu @ t�?}*i TL�?| {W 5 W+qc ?@4i*){Wq ' $q @?_ {Wl ' f> l ' �> = = = > q� �=

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Page 31: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 32: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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Page 33: Harsanyi Power Solutions for Graph- restricted Games · 2017. 5. 3. · Harsanyi Power Solutions for Graph-restricted Games René van den Brink Gerard van der Laan Vitaly Pruzhansky

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