Program
Standard Talks, Mornings  AUDITÓRIO 2, Quelhas
Working Sessions, Afternoons (14:0018:00): Rooms  CTT, DELTA, IAPMEI, 306
List of Participants: Adam Atkinson, Alda Carvalho, Alexandre Silva, Annamaria Cucinotta, Antoine Dailly, Bernhard von Stengel, Carlos Pereira dos Santos, Cátia Lente, Fionn Mc inerney, Hironori Kiya, João Pedro Neto, Jorge Nuno Silva, Karim Soliman, Koki Suetsugu, Kyle Burke, Marc Heinrich, Matthieu Dufour, Matthew Ferland, Melissa Huggan, Michael Fisher, Ravi Kant Rai, Richard Nowakowski, Svenja Huntemann, Thane Plambeck, Tiago Hirth, Tomoaki Abuku, Urban Larsson, Valentin Gledel, and Yuki Irie.
22/1  Tuesday  23/1  Wednesday  24/1  Thursday  
8:308:45 
Opening ceremony 

8:459:00 
Richard Nowakowski, Dalhousie University, Trends in Combinatorial Game Theory 

9:009:30 
Yuki Irie, Tohoku University, pSaturations of Welter's game and the irreducible representations of symmetric groups 
Tomoaki Abuku, University of Tsukuba, On NIMlike games played on graphs 

9:3010:00 
Antoine Dailly, University of Grenoble, Connected subtraction games on graphs 
Thane Plambeck, Counterwave inc, Shotgun wedding: ECGT + CGT 
Svenja Huntemann, Carleton University, Enumerating DOMINEERING 
10:0010:30 
Michael Fisher, West Chester University, Beatty Games: Big and Small 
Alda Carvalho, ISEL & CEMAPREUL, Combinatorics of JENGA 
Valentin Gledel, University of Lyon, The MakerBreaker domination number 
10:3011:00 
Coffeebreak 
Coffeebreak 
Coffeebreak 
11:0011:30 
Carlos Pereira dos Santos, CEAFELUL & ISEL, Extended Combinatorial Game Theory: the effect of the terminal move 
Koki Suetsugu, Kyoto University, Dependent sum game: Some variants of Wythoff NIM and Ryuo NIM 
Ravi Kant Rai, Indian Institute of Technology Bombay, Optimal play in DUIDOKU game 
11:3012:00 
Marc Heinrich, University of Lyon, Partizan subtraction games 
Fionn Mc Inerney, Université Côte D'Azur, The ORTHOGONAL COLOURING GAME on graphs 
Hironori Kiya, Nagoya University, Two player TANHINMIN and its extension 
12:0012:30 
Bernhard von Stengel, London School of Economics, Computational progress on the CatchUp game 
Urban Larsson, Technion  Institute of Technology, Efficiency of cumulative subtraction games as extensive form games 
Matthew Ferland, University of Southern California, Computational Properties of SLIMETRAIL 
12:3013:00 
Melissa Huggan, Dalhousie University, The Index: a measure of equality


13:0014:00 
Break for lunch 
Break for lunch 
Break for lunch 
14:0018:00 
Working sessions 
Working sessions 
Working sessions 
19.0023:00 
Conference Dinner 
Alda Carvalho, ISEL & CEMAPREUL, Portugal
Title: Combinatorics of JENGA
(Joint work with Carlos Pereira dos Santos and João Pedro Neto)
Antoine Dailly, GSCOP, University of Grenoble, France
(Joint work with Julien Moncel and Aline Parreau)
Title: Computational progress on the CatchUp game
Abstract: We report on computational progress on the game «CatchUp» analyzed by Isaksen, Ismail, Brams, and Nealen in 2015. Two players pick and remove numbers from the set {1,...,n} according to the «catchup» rule that says you pick the next number as long as the sum of your numbers is less than that of the other player. After that (having reached an equal or higher sum), players switch. The player with the higher sum at the end wins. For n=5, for example, the first player wins by first picking 3. With oldfashioned memorysaving coding but large computer memory, we extend the computational analysis for optimal play from maximally n=18 to n=28. The following pattern emerges: When there can be a draw (when n or n+1 is divisible by 4), there will be a draw, and when there cannot be a draw, for n=21 or larger the first player wins with the first picked number no larger than 3. (For n=9,10,14,18 the first player loses, which seem to be the exceptions.) Further computational analysis may help in eventually finding an induction proof to prove this in general.
Carlos Pereira dos Santos, CEAFELUL & ISEL, Portugal
(Joint work with Richard Nowakowski and Urban Larsson)
Fionn Mc Inerney, Université Côte D'Azur, France
Hironori Kiya, Nagoya University, Japan
Koki Suetsugu, Kyoto University, Japan
Title: On Wythoff type extension of general subtraction game
Abstract: Cyclic NIMHOFF is a variant of Wythoff NIM. In this game, there are some heaps and each player can move as following:
(i) Choose one heap and remove any number of stones.
(ii) Remove a total of k stones from any number of heaps, provided that k<p.
Fraenkel and Lorberbom found a formula to obtain the SpragueGrundy values of the positions of this game in 1991. (i) is the same move as NIM and in this talk, we replace (i) with the move of other games like subtraction NIM or allbut NIM. We include the case that replaced rules are different for each heap.
(Joint work with Tomoaki Abuku and Ko Sakai)
Marc Heinrich, LIRIS, University of Lyon, France
Title: Partizan subtraction games
(Joint work with Eric Duchêne, Richard Nowakowski and Aline Parreau)
Matthew Ferland, University of Southern California PhD Program, United States of America
Michael Fisher, West Chester University, United States of America
We will also report results for the nonatomic version, where the left and right subtraction sets are given by {α} and {β}, respectively.
Octal games are impartial games that involve removing tokens from heaps of tokens. These types of games are interesting in that they can be uniquely described using an octal code. Historically, research efforts have focused almost exclusively on octal games with finite codes. We consider octal games based on infinite octal codes where the heap sizes corresponding to elements of a Beatty α sequence are played according to some fixed removal rule and the heap sizes corresponding to elements of a Beatty β sequence are played according to some other fixed removal rule. Interesting periodicity seems to occur in most cases.
Melissa Huggan, Dalhousie University, Canada
Title: The Index: a measure of equality
Abstract: Playing combinatorial games with simultaneous moves naturally introduces a probabilistic element to game play. This small change to game play forces big changes when we consider the underlying theory of simultaneous play combinatorial games. In particular, understanding how to interpret equality of games has been very challenging. Throughout this talk, I will present a refinement on the expected value, called the Index, which captures the notion of equality for simultaneous play combinatorial games played under continued conjunctive sum with the extended normal play winning convention.
(Joint work with Richard J. Nowakowski and Paul Ottaway)
Ravi Kant Rai, Indian Institute of Technology Bombay, India
(Joint work with K.S. Mallikarjuna Rao)
Richard Nowakowski, Dalhousie University, Canada
Svenja Huntemann, Carleton University, Canada
(Joint work with Neil McKay)
Thane Plambeck, Counterwave inc, United States of America
Title: Shotgun wedding: ECGT + CGT
Tomoaki Abuku, University of Tsukuba, Japan
Title: On NIMlike games played on graphs
Abstract: We study «NIM on graphs», an impartial game played on a finite undirected weighted graph. In the starting position, a piece is placed at a vertex of the graph. Each player alternately moves the piece from the vertex to one of its adjacent vertices and decreases the weight of the edge to any strictry smaller nonnegative integer. The game terminates when one player has no moves and then this player loses. We give the winning strategy and the Grundy values for positions of the game.
Urban Larsson, Technion  Institute of Technology, Israel
Title: Efficiency of cumulative subtraction games as extensive form games
Abstract: This is an extension of a talk on Cumulative Subtraction Games (CS). Zermelo's backward induction provides a foundational theory for both combinatorial game theory and classical game theory zerosum extensive form games, in that the optimal play can be computed, although the generic complexity provides little hope for the algorithmically inclined, since the number of terminals grow exponentially with the depth of the game tree. Some time ago, we displayed a beautifully short and efficient way to compute such optimal play outcomes, for the class of 2player symmetric (impartial) CS games. Now, we answer the question, precisely how far does this approach generalize to generalsum extensive form games. The second part of the talk reveals that, in fact nplayer Cumulative subtraction games are in bijective correspondence to classical extensive form games. We finish off by proving that, in the case of 2 player symmetric CS games, the selfinterest optimal actions are identical to those of the analogous zerosum variation, if the reward function is increasing.
(Joint work with Reshef Meir)
Valentin Gledel, LIRIS, University of Lyon, France
Title: The MakerBreaker domination number
Abstract: The MakerBreaker domination game is played on a graph G by Dominator and Staller. The players alternatively select a vertex of G that was not yet chosen in the course of the game. Dominator wins if at some point the vertices he has chosen form a dominating set. Staller wins if Dominator cannot form a dominating set. In this paper we introduce the MakerBreaker domination number of G as the minimum number of moves of Dominator to win the game provided that he has a winning strategy. This parameter is compared with the domination number and residual graphs are introduced to determine the MakerBreaker domination number of an arbitrary tree. The invariant is also obtained for cycles and bounded for union of graphs.
Title: pSaturations of Welter's game and the irreducible representations of symmetric groups
Abstract: We establish a relation between the SpragueGrundy function of psaturations of Welter's game and the degrees of the ordinary irreducible representations of symmetric groups. We present a theorem on these degrees, and using this theorem, we obtain an explicit formula for the SpragueGrundy function of psaturations of Welter's game.